dehumidifier
A 1 kW constant electrical load does seem excessive for a 12 v automotive system.
Consider getting a dehumidifier to run off of the inverter and 12 v battery bank.:
**broken link removed**
The dehumidifier also uses a freon compressor to achieve its dry air product, but it is more efficient than an AC compressor, and would not be running as frequently. Maybe it would have a battery current drain of something like 50 amps, compared to Reloadron's 84 amp figure, mentioned previously. Here again, the dehumidifier should not see as many compressor on hours as the AC unit.
The savings in gasoline used to recharge the batteries using a dehumidifier could be significant.
You might not have air conditioning, but you could maintain a reasonable comfort level ... if you don't open the doors too often.