Larry,
As far as I know the Converter is 80-100 Amps depending on year. I wouldn't call 80 Amps a trickle charger. Trickle chargers are in the 1-8 Amp range. BatteryMINDer makes a very good trickle charger.
Turn the disconnect key to so it can be removed, and I think you can trickle charge the battery in the Montana. The remote control will pull some power, but not enough to worry about.
You could have a bad cell in the battery, cause it to not charge all the way (most likely reason). You can get a Battery Hydrometer (around $10 at any auto parts store) to test each cell holding a charging.
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