This might be the issue. The rules are "All movement is performed simultaneously." (pg. 33 LBB1). You seem to have adopted some initiative system and applied that to movement which makes it not simultaneous but reactive.
Personally I've never had any difficulties with some reactive type combat resolution. I just have everybody move
OR shoot in order of Dex (no dice rolling or initiative unless surprise happened to both sides) - highest to lowest on both sides of the combat. It can be chaotic that way but it makes more sense than taking turns and its more interesting.
This sometimes means the fastest players might make the worst choice, but then the slower guys get to change their minds before their turn comes up....I feel this is ok in even a ten-second round since it all comes out the same in the wash most of the time - the faster guys also hit more often while the slower ones don't. And I like a more "cinematic action-adventure" kind of resolution so...
...if Dirk Deadeye goes down in a blaze of gunfire, then the guy whose turn comes up next might decide to run instead. Likewise if the group of Marines comes barreling around the corner with blood in their eyes and the first two go down from a couple of RAM grenades the others are more likely to dive for cover than keep doing what they planned before (keep running out into RAM grenade fire and all die) as would happen if it were all simultaneously resolved.
And to do true simultaneous action combat you have to have everyone write down what they intend to do and then set it all up each round...otherwise you still get the same effect as just doing it in order of DEX with some people who are later in the order changing their minds. Going through that would so slow things down that my players wouldn't have to rebel - I'd throw myself out the window.
Melee combat (this includes animals attacking - but the animal are always considered in melee mode)) is only swinging and poking and movement is part of the process, so players in melee can move
AND swing in the same turn with no penalty. Sometimes with melee you want to get closer for a better DM to hit, but in a gunfight you usually want to get farther away or behind something.
I also allow (CT heresy warning here) one parry roll in melee combat or evade. It's Runequesty but if you evade then its an auto -2DM to hit you...but you can't swing back. You're just ducking and weaving and looking for a way out or something. Good if you are unarmed and can't get away yet.
If you parry then the roll is same as your attack roll. If you parry you don't take damage - sometimes this means just a lot of swinging and slashing, but eventually someone messes up and that first slash starts the process: oops, lost your +DM to hit...ow, now your getting hit more often and can't defend too well, ...and now your dead. And my players prefer it to the feeling that they are just like a couple of old Prussian Schlager duellists trading blows while standing in place.
Also I do attacks and damage simultaneously and applied effects each turn, including reduced characteristics affecting performance.
This is why I don't use simultaneous combat rules - they don't reward the more skilled combatant, or reflect just plain luck very well. If it all happens at the same time then why bother with dexterity or initiative rolls?
I seem to also recall taking the Animal Speed as its "walking" speed and allowing +1 (or more? double maybe? don't recall for sure) to it for "running" just like characters get. It is very difficult for a person to outrun most animals that will chase, and very difficult for a person to outrun most animals that may be prey to chasers.
Or you can do like I do and have two speeds per animal - one speed is their usual "walk"...but the second speed might be 1-3 higher, but depending on the animal may only last for a limited time. So for example: a crocodile can outrun a man (speed 3)...but only for about 2 rounds, then the critter goes back to speed 1 - so depending on distance when you encountered it you might be able to get away. A tiger can outrun you at a speed of 3-4, for about 4 rounds, so you aren't likely to out run him at all because of the speed and time. An elephant can run at speed 3 forever practically so good luck and don't trip.
So by having two speeds and a limiter on the "running speed" it makes things a little more interesting when hunting animals in the game.
An example is my Kimpali Cheshire Cat: it is really fast, but because of its build it is only going to outrun you for one round so as long as you are at least 4 bands away and wearing your felony shoes you'll probably get away with little problem. Ranchers who find them trying to dig under the fences to get at the tasty Paisley Bison on the other side can easily down a Cheshire Cat (and extremely dangerous 600lb killer) so long as they shoot it from at least 5-6 bands away. If they miss or wound it it'll charge, but only move 3 bands for one round then tire and the rancher gets another free shot at it. Most of the time this kills the lion, but on the other hand if they encounter a Grass Manta then that thing can fly at max speed 4 for 6 turns so a hunter that is too close or a bad shot is in trouble.