I have MBTs that, IRL, nothing anyone has brought can destroy (immobilize, yes, which in this setting is pretty similar). Considering no one mentioned an issue with that, I have no issues with a guy having a stockpile of Soviet stuff, personally. Pretty common with preppers on a budget anyway.
In terms of populations - it might be a good idea to have people establish what they are. I kinda figured the Dragoons were quite a bit BIGGER than most of the other groups - like, 80 members minimum, closer to 300 maximum. I can go into how I arrived at that number if it matters, but to put it simply, it's a reasonable approximation of how many people would be required to keep a few tanks, a half dozen LAVs, and two or three trucks operating and still somewhat practical to drag around. It was intended as a major strength (that's a lot of guns) and a major weakness (that's alot of people to feed). Reading over the stuff the others wrote, I figured this would likely be bigger than most of them except for long established communities or towns.
I don't mind adjusting and chopping things down (or leaving it too, if that's smaller than how others invisioned their populations), but that's why I suggest establishing some rough numbers.
In terms of how to run it - I'd maybe suggest breaking it up into "days" divided by "periods".
In period one, Group A could say "Today, I want to send x amount of dudes to look for something, and y amount to increase the defenses, while z amount tends the fields". You could then roll to see how each did, based on the manpower dedicated to the task and roughly on the skill of the group in that area, and throw in some events for really good or really bad rolls (as an example). I think a lot of that sort of stuff could be done fairly narratively.
It might also be good to establish how PvP will work, as well as PvE. I don't have a great suggestion for this that doesn't potentially hold up the game for people not involved in a fight, but the one thing that does come to mind would be to have a second phase after the actions above. So, for example:
Group B says "We want to dedicate our military forces to securing 25th Street and Smith Ave (which could be a particular zone or grid on a map)." Group C could say "We want to put all available manpower into also securing this, even if it means pulling people off other things."
Once all the other groups non-combat actions have been rolled for period one, these two get to go at it. You could roll for "initiative" or base it on military rating and other factors (one group is next to the location, the other has to cross part of a city). Whoever gets the first action could decide to attack or defend (i.e. write out their moves first or second). They'd lay out their plan, the other group would lay out a response, then based on stats, point allocation, dice rolls and how well thought out the plan is, damage could be dealt to "hitpoints". That would be end of period 2.
Assuming one side won, either through HP reduction or because the other side decides to withdraw, the two teams would spend period 3 deciding how to conclude their actions (i.e. how to secure their new territory in case of counterattack, or how to regroup after defeat, or simply going home to spread the bad news). If the fight is not conclusive, they do not partake in period 3, and have nothing else to do for the day.
For everyone else, period 3 would be spent dealing with whatever the results of period 1 were - if trying to dam a river causes flooding, then they could evacuate, or try to stem the flow, or whatever. This would really just be pretty much the same thing as period 1 mechanically, but gives everyone a chance to always have something to do by not making their actions rely on interacting with the other PCs or being only combat related.
The day would then end, starting all over.
It's a complicated system, maybe, but there's a few advantages - it allows everyone to play "simultaneously", and not have to wait for others to decide what they want to do, and while kind of slow paced, might work ok on a forum (where pacing is hard to set). It also stops military factions from hyper-aggressively stomping everyone into the dirt with a simple dice roll, as there's twice as much time allowed for actions and reactions (running away, making peace, setting a trap, whatever).
Obviously, exceptions to the structure would be made where logical - if PC faction A is talking to PC faction B, each conversational post shouldn't really count as a whole period. Just a suggestion. I don't really care how we do it to be honest and have run exactly one RP in my life, which ended in failure (because I had too many mechanics :) ).
The other suggestion I'd have in terms of mechanics would be to use grid maps. There's some advantages there too, but more than anything, I just really like maps. As I said before, I'd be happy to make some if you need a hand, and once a location/general game scaling is decided on.