Sigg, I like this. However, I agree with soloprobe it's undergunned. Remember in a "standard" Mayday encounter it will be taking on an equal tonnage in enemies, so it should be able to fight 12 enemy Scouts to a standstill.
The instant-kill rule works both ways, and you don't want a Kinunir destroyed in one turn by concentrated fire. This can only be prevented by defensive measures. Even though it has 4G, in practical terms it should be moving at 1G with M3 active, providing a -3 DM to incoming fire. Additionally, one of its turrets should launch sand, giving it -6 total to laser fire if it doesn't maneuver. That should keep it from taking four laser hits in a single turn.
Which leaves missiles. Sand and M3 will give it a -4 for missiles to hit, but a missile will still hit on an 8+. Considering it could be taking a lot of missile fire, that's not a great defense.
Which is why I think it needs more lasers. Six at least, for the primary purpose of anti-missile fire. Remember that if it doesn't use its shift DM modifier, it can continue firing on a new target after destroying a target, so it can destroy multiple missiles with anti-missile fire.
Since the number of missile launchers is irrelevant in Mayday, I'd keep its 6 missile launchers. I'd also keep its 8 dual turrets. But instead of giving them each beam lasers, I'd give them one beam laser and one sandcaster. That gives it 8 lasers and 8 sandcasters. Again, more than one sandcaster is irrelevant in Mayday, so this is a way to keep the ship "official" in regards to traveller but maintain some play balance for Mayday. And then I'd keep your Particle Accelerators.
I like your Particle Accelerator rule, but I'd add that they're uneffected by Sand, and that one of the hits is +3 on the damage table (radiation damage).
I'm not sure about the Model/7, since it doesn't exist in Mayday.
My version would be:
Battle Cruiser, 1200 ton starship, 4G, Model 7, 2 particle accelerators, 8 lasers, 8 sandcasters, 6 missile launchers, 1 pinnace. Programs: all, including jump 3 and jump 4.
Special Rule: A particle accelerator is treated as a laser with a -1 Attack Table DM. However, it is uneffected by sand and scores two rolls on the Damage Table with each hit, the second roll receiving a +3 DM.