Ok, again, not much has happened since last October, but a bit of progress has been made in the last few weeks:
First, I found a new board that is much closer to my desired specs (it uses the Samsung 2410X that I was interested a year ago and includes a CrystalLAN CS8900A providing an ethernet port). The board, the LN2410SBC from ClabSys, costs $250 in quatity 1 from the U.S. distributor, LittleARM, but the documentation that I've seen so far is a bit sparse.
Second, I've found a neat way to build a custom, multi-output power supply: Texas Instruments makes these neat little, self-contained switching power supplies in DIP packages. You can pretty much build a power supply as if you were plugging together lego blocks! Sure, you need to add a few passive components (bypass caps and a couple of pullup resistors on the regulated devices) but it's a hell of a lot simpler than building a buck/boost supply from NatSemi Simple Switcher, which come in nice TO-220 and DIP packages, but require external inductors, or the Maxim/Dallas parts, which usually come in surface mount packages and require external inductors. In either case, the circuit layout for a good switching supply is non-trivial and the TI parts have it all done for you.
Anyhow, with the TI parts I can, relatively quickly, construct a power supply that will provide logic voltages for both the SBC (5V) and the LCD (3.3V) as well as the LCD bias voltage (-36V) and 12V for the CCFL inverter. Right now I'm putting together tools to etch and drill simple circuit boards.