I came to an idea of an addition to the current system-
recruit training- that way you would have unlimited supply of soldiers but you would have to train them from the beginning. How would it work? You have virtually unlimited supply of people willing to become a part of phalanx. There would be a recruitment centre where first selection would take place- health tests including viruses tests
and other prerequisites for future soldiers (this part would not exist at all, the base structure would be needed just to access recruits.
After that the special big structure (2x1 tiles, as 2x2 would be to big[2x2 means four squares]) would be needed to start training. That way you will never get soldiers with stats higher than 20, but you can stress some aspects more than others- before you start training you chose if its going to be a sniper (with 20 skill, lol) or a heavy gunner or an assault meat. Training takes some time- for game balance lets say 25 days and credits as you need to give them food, living space and so on - maybe 2x2 barracks is not that bad idea as it would contain training space and living quarters.
Barracks would supply up to 20 recruits at the same time. After the training they would be available to transfer to specific base. This would make also another specialised base- training centre.
Of course all stats and sizes are just my guess- feel free to tune them to your liking.
Nothing would change with the normal soldiers- you could still hire some veterans from nations, but my solution would help with the soldier shortage in some circumstances.
PS maybe highly specialized training would bring one stat to 30, another to 20 and the rest to 10-15 randomly?