What's the strongest single deep cell12 volt battery?

http://www.atbatt.com/battery-tender-power-tender-plus-022-0157-1-12v-5a-battery-charger.asp

Yes this charger should meet the battery specifications.
The 5 amps might prove a bit slow if using a generator.
Biggest issue is charging must be limited to 24 amps, I suggest 20 max. Converter is probably 50+ amps.

Leoch LPG12-100 charging specs

A solar panel charging at 8 to 15 amps might be the ticket in the future.