Here's an idea I've considered......Find a hi-capacity UPS. Most use a 12V battery inside (all the ones I've taken apart anyway). Tap into the 12v wires inside the unit, using this 12V to power the PICO. The UPS own charging circuit will recharge the battery.
This should work ok. The part I don't know about.......will the output to the PICO when the computer is running, be too much for the charging circuit of the UPS? Don't know.... :?
I'd say it probably depends on the type of UPS. Offline and line interactive (the more common consumer type) UPSes might not be built to handle the heat output of constantly chargeing the batteries/powering the Pico PSU. After all they are supposed to charge the batteries once and then just keep them happy by trickle charging them.
On line UPSes on the other hand should have no problem at all with this since they always do AC->DC->AC conversion while running on line power.
Oh and another thing, I think high capacity UPSes usually has two or more 12V batteries in series. Drawing power from only one of them might cause problems since the charge level would differ between the batteries.