I would first of all get some sort of instrumentation to accurately measure what your power consumption is and get some idea of where your battery states are at. Something like a trimetric is fantastic, but even just a decent voltmeter and ammeter would be a big help and is fairly inexpensive. You'll use this no matter what you end up doing.
I would guess offhand that two pairs of GC2 batteries would very well get you through four days of conservative usage without becoming excessively discharged, and a large converter (80-100A) could bring them back up to 90 percent or so in three or four hours. Alternately, a single pair of batteries and sufficient solar power (maybe 200W or so?) could likely keep you going nearly indefinitely if you have reasonably open skies. I want to emphasize that these are at best very very rough guesstimates, barely better than order-of-magnitude computations.
If you find you need more battery capacity than you have space for, you might want to investigate GC12 batteries. These are 12V golf cart batteries, somewhat longer and heavier than GC2s (but of a similar width and height), and a pair of GC12 batteries has about half again more energy storage than a pair of GC2s. If the shape fits your mounting space better, this could give more battery capacity...though unfortunately rather less economically, as the price per watt-hour favors the GC2s.
