I made the exact switch as you propose over 9 months ago without adding batteries (I have the same amount as you). It's the best thing I've done to my RV! It takes less amps than the old Dometic. I only noticed a .2 voltage drop overnight.
Good luck, you'll wonder why you didn't do this earlier!
Mine did this last summer and all it turned out to be was a broken power wire to the motor. It took longer to get the unit out to remove the back and repair the wire where it broke off at the spade connecting it to the motor. Simple fix only cost 15 cents for a new spade.