I don't see how it's a problem for you that people from the CR are in the MR
It used to bother me, but tbh part of the reason I bring up these ideas is because when there's a more tangeable objective like bases to be sieged, territory to be kept or lost, people can belong to multiple factions, but you can only fly for one at a time. When it comes to these battles, players would get the chance to back a side they prefer or simply join in where they feel needed. In theory if there is opportunity for gain on both sides, it seems likely to balance out equally. But of course there will be some imbalance in places, in a war you want to keep the balance in your favor. For such wars, I feel NEMP's were perfect balancers for smaller factions.
In the case of the Outcasts vs CR, I would find it interesting if the CR cap bases were attackable in real time, and outcasts go raid here and there. Thats also why I suggested that factions with shipyards get to replace 'destroyed' ships within a week or so for another go, and if the movements were guided by the system and updated by the devs with patches, if one side loses a bit, its not over. But maybe CR would lose territory in Tau-31 for a while? Then regain it a month later? Say the ship by Harris is taken out by players after a few days or weeks of attacks (depending on how well defended, and the stronger they are the better) and they lose the planet...? In theory they could focus a group of battleship bases from Coronado to move up in a series of moves from point A to B to C over the course of a few weeks, and try again to move on Harris. One ship may fall easy but a group wouldnt. Players could try to stop them all the while, and defend. Bear in mind, they might have other areas to protect in other systems from other factions. Every faction with caps would be in the same situation. Thats where forging agreements with other factions would be important, to cover your rear!
I also think of the Enclave. They have a planet and a shipyard, so you'd think that would pose a theat and provoke another war. I say, let them try to expand, get more ships, while if made attackable, they'd also be losing ships, so how well they do is up to the players. Same goes for Bretonia.
So the chance to expand comes at the cost that in some cases factions like Enclave could be finally defeated or be reduced to secret bases in isolation. On the other hand, with a strong player base, they could keep Bretonia on its toes for years to come.
All the while, these battleships could be buying munitions or arms at a high price and basically foster supply events at the same time. That is also a perfect chance to add extra scores to battles, like each 100000 units sold might give a faction a point or special right to be used in the battle. Essentially, players would be a swarm that follow and defend their sides' ships, while also branching off to try and attack the other side. Under the battle system, every faction has a chance to expand or stengthen themselves, make small or big moves, and recruit people for various jobs and the real need to work on goals.