Since this is a bicycle forum, put an old bike on a trainer, rig up a 12V generator and something to condition the power.
$30 for a 7AH 12V SLA (sealed lead acid - standard back up battery) is a little steep. You should be able to enter the model number of the router and find an exact replacement from any of several sources. I've had good results with Batteries Plus (brick & mortar) and batteryspace.com (internet). There was another source I found on Ebay (can't recall the name - sorry) or Amazon (maybe you can get the free economy shipping?). These are standard replacement for computer UPS and the portable "jumpstart" car systems.
You could plug the FIOS router into a computer UPS; now you have comercial power, the external UPS, and the internal battery (once replaced) before you loose service.