Yes measure compartment including access door and squeeze the biggest one you can fit in there. Batteries come in many shapes and sizes, you are not limited to any two standard sizes. I'd start with Mr. Wizard's suggestion of the Trojan 1275 to see if it would fit. That would be a wonderful upgrade. You will need to pour over spec. sheets.
Also if you're having power problems, don't hesitate to check out LED lighting, LED screen TVs, and newer tablets or low consumption laptops if any of those apply. Working from the demand end is just as satisfying as from the supply end.
I've done the same thing with mine: I have pair of Lifeline 300 AH 6 volts stuffed into my compartment. There is hardly a cup of air left in the entire compartment.
