leadbelly,
I'm running into the same issues that your are and have been thinking about this for a while. The small dehumidifier that you indicated is a peltier device and they aren't very efficient. Same device that is in the thermo-electric coolers. I had toyed with ganging up several peltier chips with enough heat sink to cool my small area. There are plenty of these chips and devices available on eBay. Just didn't seem to be able to live with the theoretical power draw.
I did see a small compressor based "personal air conditioner" that supposedly generates 1000btu with a 2.1 amp draw at 120v for a consumption of 250w. That's less than the Pet Cool. The unit seems to be a cross between a small AC and a dehumidifier and dumps the heat off the backside of the unit for no net cooling. BUT...if you could dump that heat outside as you suggested it might work. It's a relatively large unit and costs about $200 but it draws less juice than the Pet Cool and it does do work as you can see from the dehumidification specifications. As others have indicated, you would still need some battery behind the scheme, perhaps double your battery capacity. Check out: Amcor model APC 2000E.
http://www.amcorgroupusa.com
J.B.