You definitely need moe charging capacity, for AGM batteries like you have, figure on ~2% self discharge per day - you'll need to replace that even if you don't use that battery at all so the 18a/hr battery will need to be 'fed' about .36a/hr daily to maintain its charge. Also figure on only drawing down 50% of the battery capacity for decent battery life, the 18a/hr would be able to provide 9a/hr or 96w/hr before needing to be fully charged. Also, avoid "deficit" charging where you never fully charge the battery from the previous days' use. That will cause sulphation on the plates effectively ruining the battery, particularly AGM's since they can't be equalized like FLA.
Got that right - electrical circuits will try to maintain power [watts] at a constant level. If voltage drops, amperage increases to maintain the wattage level.
I used to work for NEC in the Fiber Optic Transmission division. The designer of the power module for one of the fiber optic multiplexer models forgot to include an under-voltage cut-off circuit in the power module.
Note: The under-voltage cut-off is a mandatory BellCore spec.
Anyway, New York Telephone [now Verizon] performed the BellCore under-voltage protection test when it installed 100 of these multiplexers in a new Central Office installation.
They dialed down the voltage and ALL 100 power modules FRIED !!!