Sorry Hugh, there is no free lunch.
to run your fishtank as you last describe, you're going to be charging that battery at a constant 25 amps 12 VDC, as thats what a ASSUMED 300 watt load at 120VAC output of the inverter, is going to draw out of the battery.
~25AMP X 12 VDC = 300 watt load at 120 VAC
so no free lunch..........and Mr Battery is going to get boiled dry fast at a constant 20-25 amp charging rate
web links:
Inverter Realities - SailNet Community
http://redarc.com.au/handy-hints/tech-tips/inverter-current-draw