It might be appropriate to first examine what the Squeezebox 2 says about itself -
http://www.slimdevices.com/pi_specs.html Power
Power input
5.0V DC, regulated
Center positive, sleeve ground
Connector: 2.5mm ID, 5.5mm OD, 11mm long
Min supply rating: 1000mA
Power supply
Switching power supply included
Input voltage range and plug style specific to shipping destination
Power supplies are small, efficient, and do not get hot
One of four styles is included depending on country

Soooo, examining the supplied overbuilt switching wall carbuncle, one might posit that it might bear improvement. (this is not to say that excellent switching supplies for audio do not exist, and will become more common in the future. I'm simply stating that the supplied unit isn't one of them.
Offhand, you've two options -
1.Use a 6v SLA/charger and drop/filter the voltage
2. Put in a proper linear 5vdc regulated powersupply, no wretched toroidal transformers, but a proper split bobbin transformer. A typical 3amp regulated supply with overvoltage protection is rather generic, and at the typical retail of $35, one might be tempted to scratch build for increased peformance, but I happened to see a bunch fall off the back of a truck & for less than $10, its a 'Sarah Lee'. And Felicia-cizing would certainly improve upon that. As you're already using a proper 'back end' transformer (the linear supplies), one additional appropriate transformer with flitering cap(s) and Bob's yer uncle.
This is the non-invasive $35 first cut. Obviously if you're willing to crack the box, further joys await. If someone would send that squeezebox to JoshK, I'm sure we could work something out....
Two dedicated linear power regulators for DAC and line-out stages
Full 6.0Vpp line-level signals
This confuses me a bit. If both those linear regulators are the expected 3 pin jobbies providing <5Vdc, the only way the line-level could provide 6Vpp is if the output stage were a BTL, bridge tied load achitecture. or
There is a voltage stepup in the box to provide either a split rail, of a higher single rail to provide the stated p-to-p output swing......
Anyone have any info on this?
In any event, if one is willing to open the box, the inevitable output electrolytic coupling caps should be upgraded, the generic 3 pin linear regulators could be upgraded, better ps caps and Saints Preserve Us, ERS could be appropriately applied.....
Regardless, providing a proper 5VDC, whether via the wall or a battery is the maximal bang for the buck, non-invasive, easy mod whether for digital or audio output.
Josh - normally I'd agree with you on simply front ending it with a Felicia, but I had the advantage of seeing the external ps, and yes, size can be decieving, Its a testament to miniturization and the economy of mass production, but that is simply not a proper ps to work with.
FWIW