kbear99, alkaline cells are a bad choice for medium to high drain applications. I guess your heated socks may drain the cells in less than an hour, which in practice is just a little above 3.2V average at 1A discharge for 3 cells in series. What this means is you would get a little more power output and much better runtime using 3 li-ion 14500 cells in parallel.
If you go the LiFePO4 route power output is likely to get much higher (well above 3x), runtime will suck and it may even collapse (because of heater element failure).
4x AA Ni-MH would work good.
Cheers 