Well... here goes.
I thought perhaps there could be some sort of Supply Transportation Service(SPT) run by the Army, a bit cliche, but certainly a most necessary thing. Safe houses like the Museum, the Library and the Church definitely don't have as steady or reliable supply of food as the Subway does, and even the Subway could eventually run out of supplies (not to mention the soldiers would have to guard the stores like hard-asses when they reached a check-point stop where shops and supplies are available).
So a SPT. They transport necessary supplies, mainly food and medication but also perhaps from time to time a few luxury items like toilet paper, blankets, pillows. Alcohol would be prohibited but there's always the corrupt individual who wants to earn a spare buck by peddling the items on the street.
No clue what type of vehicles could be used for these. There could be the small supply vehicles, possibly army jeeps, that could carry the bare essentials and make rounds to be sure all safe-houses are stocked. They can then contact the main hub that controls the SPT to notify that a certain safe-house needs a supply of food, medication or any other necessary need and the main hub can then deploy the big SPT vehicle. Perhaps some kind of armored truck that can carry a lot more.
Another way to make the SPT more interesting would be that it can be a possible job for Soldier characters, but they perhaps need to apply for a job change (if they don't already have it).
And yet another thing is that there could be a lottery set up for civilians so they can 'win' a spot in one of the vehicles for transportation to a safe house. Small vehicles could carry... say.. one civilian, and large vehicles can carry two - three. I don't know what a civilian would have to do to get a ticket, maybe they'd just offer it for free, since it is the army and all. Each civilian is permitted one ticket if they want to move to another safe house, of course the civilian's can barter and trade and sell between themselves to get extra tickets if they want. I'm sure the Army would generally frown on this but they wouldn't prevent the person who won from riding with them.
Edit: Link to british standard issue armoured vehicles (among other things)
here.
So... that's it! That's all I've come up with.