Li-ion is really not all that expensive anymore, and you can buy protection PCBs for multi-cell packs and intelligent chargers that are all fairly inexpensive. Going from 12V>120V>12V/5V with an inverter driving the existing PSU is a LOT of extra losses for no real benefit. Small DC-DC converters are dirt cheap now, a few bucks each so one of those for each voltage output would be easy enough. An inverting one will give you the -5V.
I think the idea is doable if you really wanted to. IIRC the SE/30 draws around 40 Watts, which would be 3-4 Amps draw from the battery. Most 18650 Li cells are good for around 500mA but matched ones can be wired in parallel. You can also get larger cells, 32500 and 32650 are about the size of D cells and good for quite a bit more current. Lithium iron phosphate and li-poly cells commonly used for RC models and high powered flashlights are capable much higher current drain without damage. Check out the RC groups and places like the Photonlexicon forums for battery info.
I think the idea is doable if you really wanted to. IIRC the SE/30 draws around 40 Watts, which would be 3-4 Amps draw from the battery. Most 18650 Li cells are good for around 500mA but matched ones can be wired in parallel. You can also get larger cells, 32500 and 32650 are about the size of D cells and good for quite a bit more current. Lithium iron phosphate and li-poly cells commonly used for RC models and high powered flashlights are capable much higher current drain without damage. Check out the RC groups and places like the Photonlexicon forums for battery info.