The biggest thing for powering from batteries, is the CRT. How much load is it drawing on the 12v rail? Also a 12v battery would do fine on a 12vrail, using power-factor correction, At the cost of some excess current.

Basically you bring the 12V in, and step it up, say 24v. then step it all back down into various voltages from that point.

the LM series is ok, but its only good for a couple of amps or so. Anything larger, you have to go custom.

Best place to look is ITX power supplies that run from 12v, and produce all the ATX voltages required.