According to my apex, it's about 6a with everything (including heater) on. The wiring doesn't scare me, there's a lot of electricians in my family who will help if needed and I am no stranger to electricity or wiring (I'm an auto tech). FWIW I put in the circuit that the tank is on now. I am thinking of putting 4 to 6 deep cycle marine batteries. I would really at the most need it to last for 6 hours as we rarely travel and even more rarely go more than a few hours away.
Ah okay, sounds like you have a pretty good handle on this stuff. Yeah I'm sure you'd be able to hook it up to the circuit. That 30A box will probably be the best bet.
So 6A at 120VAC is around 720W. Any inverter of 1,000W or higher would probably work just fine. A 2,000W inverter might be best to give you some wiggle room in case you upgrade your aquarium in the future. The big challenge will be the battery capacity. At 12VDC, 720W requires 60Ah of battery. The faster you discharge a battery the lower the real-world capacity is going to be.
I have a 100Ah battery, but
according to the manufacturer, at a 60Ah draw, the battery will only last for one hour and provide a total of 60Ah, not the 100Ah for which it's rated.
If we account for battery depth of discharge of 80% and add a 10% buffer for inefficiency, your system would need around 82Ah to run ((60Ah / 0.80) * 1.1 = 82.5). If you got five of the 100Ah batteries I linked to above, then the current draw from each battery would be around 16.4Ah (82 / 5), provided the batteries are wired correctly and discharged evenly. The manual says that those batteries will last for 5 hours at a discharge rate of 17Ah, so five of those batteries would last you around 5 hours. You might be able to get 6 hours total out of them, but you might be discharging the batteries below 80%, which could cause premature wear.
Any equipment you could have your Apex shut off in the event of an outage would reduce the battery requirement. Aside from being a little expensive though, it's totally doable to run your entire tank for a few hours on power failure.