Hi jk_and_dog,
Sounds like it may be time to get rid of that Dimensions inverter/charger. Could be a shorted SCR (silicon controlled rectifier) if it stays at 14.6 volts all the time or it could be applying an equalizing charge inappropriately. I love how they get around calling it a modified sine inverter by saying "Quasi-sine wave, with waveform stabilizer".
Normal float charge voltage should not be over 13.4 volts to prevent boiling away the water in the batteries. Monitor the voltage for a while to get a feel for what the charger is doing and then decide how to tackle any problem.
Here is a link to the Dimensions inverter/charger used by Winnebago.
http://www.airpaxdimensions.com/RV_12V_1600_3600.html
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Have Fun!! Mark & Donalda 04 Horizon 40WD no TOW 90,900+ miles and counting
Triumph Bonneville & Susuki S40 on the back