First, I quess it all depends on how we think expansion occurs.
That's important, of course, but just as important are the few scattered bits of historical information we already have. If they say that Mora got its first settlement in 60, we have to explain how Mora got its first settlement in 60.
Several of my comments were on points were you seemed to me to be contradicting canonical facts or making unwarranted assumptions.
The main problem with the Imperium's rapid expansion into the Marches is that interstellar travel is expensive. I mean, you may think it costs a lot to move people over to the star system next door, but that's just PEANUTS to moving them a couple of sectors. As for trading with anyone at that distance, the profits have to be enormous. If a round trip takes a whole year then you need a profit of about 40 or 50,000 credits per ton on your cargo. But that is only if your ships all return safely. If you lose some of them, the required profit on the rest goes up drastically.
Originally I had the notion that there were no Vargr to contend with in Corridor, Deneb, or the rimward half of Tuglikki and Provence. This would have made it possible for the Scouts to move through these sectors very rapidly, much faster than they moved towards the Rim for instance. (The Vargr would have expanded towards those regions and touched off the Vargr Campaigns).
However, T4 established that Corridor was blocked by various Vargr states, so instead I decided that if the Imperium was going to get a grip on the Spinward Marches as fast as canon had it, it would need a source of workers, colonists, and ships closer than Vland. So I made up the Lidash League, a group of old Vilani colonies struggling against Vargr raiders from Corridor and Provence and losing, the last so that they would be eager to join the Imperium voluntarily, as the Imperium would hardly want to fight a war of conquest at the end of a 40 parsec supply line blocked by Vargr.
In my opinion, expansion occurs ahead of "civilization". What I mean is, The Scouts (both government and private) enter the sector. Each has different goals. the Government scout may just be doing a survey, but the "corporate" or private scout is looking for specific things, whether it's resources to exploit or worlds to colonize.
In my opinion it does not make sense for the Imperium to expand in a planned orderly fashion into a region 40 parsecs from its border on the other side of several Vargr pocket empires.
First come the "seperatists", that is groups looking for worlds to settle, for various reasons, preserve culture, escape religious persecution, etc. Think stellar reaches ethnic groups, or David Webers "church of humanity unchained" from the Honor Harrington series. They look for T-prime worlds, preferably far from the frontier.
Heh. Your analysis matches my own quite a lot. I call them 'utopians':
1) Utopians. People who want to establish the perfect society (whatever version of the perfect society they happen to believe in). These people would want to get as far away from the Imperium as possible. And if they can just get across Corridor without falling afoul of the Vargr, the remoteness of the Marches becomes a plus.
I had another class, though, exiles:
2) Exiles. People exiled by the Imperium in connection with the pacification of various planets. Again the remoteness would be a plus for the Imperium since the exiles would be unlikely to return and cause any trouble.
These groups are especially useful because the Pacification Campaigns provide as many as are needed and can be used to justify practically any combination of number, equipment, and selection of colony world. It all depends on the Imperial admiral or noble in charge of the individual campaign. One can scoop up so-and-so-many thousands, equip them with a bare minimum of equipment, and instruct the captain in charge of the transport fleet to dump them on the first world with breathable atmosphere he comes to X parsecs from the border. Another can scoop up so-and-so many, give them a complete colony equipment package, and tell the captain of this transport fleet to find a nice, human-norm world for them[*]. A third can negotiate a settlement with the leaders of the world he's subduing that includes a choice of destination world based on the Scout reports he has access to.
[*] Though the mineral resources of said world is not important; it'll fine as long as the exiles can grow crops.

We can also use such exiles to put multiple groups of settlers on one world. In my history of Regina, for example, I have one private (exceptionally well-equipped) group arrive in 75 and prosper mightily, only to have no less than four groups of settlers dumped there from 110 to 120.
Also the "exploitist's" enter at this time. Their goal is resources to exploit. They don't care if the main world is T-prime, as long as the Asteroid belt can be mined. They also seek out civilizations to trade with. (think british colonial expansion, and the East India Trading Company, etc.) Profit motivates the expansionist.
3) Outposts. Commercial enterprises like resource extraction operations and trade enclaves like the LSP establishment on Mora. These are the true harbingers of the Imperium; the types of colonists mentioned above would mostly desire NOT to be part of the Imperium.
BUT a commercial enterprise is just that: commercial. In order for a company to invest in a mining venture 100 parsecs away, the venture must not only be profitable;
it must be more profitable than any alternate ventures available to the company on planets closer to home. As for commercially oriented colonies: What company would invest in a colony on a planet 80 parsecs away if there are plenty of good, empty planets available closer to home? I think Mora would be very much the exception rather than the rule.
Next comes the 'government' or 'institution' expansion. After the first group has opened the frontier, the 'gov's' seek to meddle (protect those primitives, interdict that world) or protect (we need a series of naval bases to keep back the ravening hordes of Vargr), or (I claim this world in the name of the Duke of Corridor [as his own personal playworld]).
Yes, and I submit that they start coming in earnest around the time Martin II launches the Vargr Campaigns.
Now concerning trade.
When the first wave of expansion occurs, settlement is sparse, trade is limited. Resource exploiter have their own haulers to transport raw materials to processing points, but eventually the distance is greater than the profit, so We build refineries on site, and ship finished materials, think steel bars vs. Iron ore. Of course this increases "Population".
But an existing population is a lot more likely to attract the first trade. It's usually so much more profitable to bring a load of TL12 goodies to a medium-tech world and swap it for stuff the locals grew or dug out of the ground than to set up a mining colony of your own.
Obviously, as population increases, both seperatist and exploiter, the need for finished goods also increases, this is where the J1, or J2 free trader profits.
The jump-2 free trader, sure. Jump-1 is just not competitive across distances longer than one parsec. It's a fact GDW didn't realize, but until and unless TPTB changes ship designs radically, it's still a fact.
When population increases to the point that the colony cannot provide for itself, that is billions of people...
TL7 worlds can support billions of people, at least as long as they're Human-norm. At higher tech levels it must be possible for any world to support itself using hydroponics and carniculture.
...then less hospitable world are colonized, that is to say the "T-norm" worlds". You know the one's, gravity's a little low for comfort, atmosphere a little thin, etc.
These become the "agriculture worlds, feeding the giants". Also as population increases, the need to relieve stress by "forced colonization" may occur. We dump the riff raff somewhere else, or give great incentives to move.
I don't believe in that trope, except as a rare and temporary situation. Relying on imports to feed a population is a logistical nightmare. It's certainly not a stable situation. And it requires the population on the argriculutral world to have a certain size.
Now, agricultural worlds supplying the elite of a high-population world with luxury food, that I can see.
(Think the 1800's land grabs in the American west, move west, get land, not the best land, but It's yours and it's better than being packed like sardines in this Arcology, Honey, pack the truck, were moving to Beverly, Hill's that is...)
As I mentioned above, moving people across interstellar distances is expensive -- VERY expensive. Moving to a neighboring world is propably no more expensive (in relative terms) than going from Europe to America was. But moving into the next subsector will cost you several years' pay, and going several sectors away is beyond most people. In order to go several sectors away you have to be fairly rich and very motivated. Unless someone else is picking up the tab, of course, but that presents other problems.
The Pacification Campaigns might produce some utopian groups fleeing from the Imperium, but more groups would be exiled (and transported) by the Imperium. As I said above, these groups are useful for explaining why some really shitty worlds were settled early while some garden worlds not that much further away were left alone; these exiles often didn't have any choice about where the Imperium dumped them.
Hans