Well sit back down and let me tell you a tale of the thing we call VEAP... Veterans crappy educational benefits program. Not to age myself, but compared to when I was in you have a much better set of educational benefits.
JD Payment - you answered it - the amount of tuition benefits you get. Attend a school that is $57,000 a year, you are still only getting $8,000 a semester paid in your scenario.
Veterans dependent benefits for my family provided them a helping benefit. $1,018.00 per month for full time at current rates, prorated each month based on course load. If you combine that with an in-state tuition and living at home, it could mean a free undergraduate degree. A scholarship and at home means cash in the bank going into grad school. It sounds though that you have to know and work your programs just as much as I do for the most effective use of that once shot chance.
I have a spreadsheet of every school I applied to, and its BAH. With just google searches for apartment rates, x12 months, and the 100% BAH E-5 dependent rate for only x8 months, it doesn't go very far. Let alone cover everything if you had a family living with and a stay at home spouse.
Columbia at $3,759 sounds great, unless you want to be close to the school. If you are willing to train it in every day, yes, you could easily get a very nice place for a family for 3 years. Well worth the sacrifice for a vet to study on the train each way for an hour while the family has an easier time during the three years.
I have been trying to use my BAH to be at my school. walking or shuttle distance. And sadly that makes me the weird old guy in some student housing type situations. But hey, that is their problem. A shared apartment with an old sailor and a well stocked fridge and a guy who doesn't keep accurate count of the liquor sounds like a dream roommate