Sudden flickering, converter going?

Not sure what are the symptoms of a converter (infamous Paralax 7300) are in it's death throes, but maybe this: plugged into shore with batteries in store, and returning at the end of the day, lights would intermittently dim and furnace fan throttled way back. Don't think the 125v circuit was affected, but the 12v circuit was acting like it was on it's last legs, if I ran the water pump, the lights would flicker in sync with the pump and kept dimming and powering back. Placing the battery in use mode seems to have eliminated the flicker and dim. I't been a while since we've been off shore power (when battery is in store), so I used a trickle charger a couple days ago to make sure batteries were up, and at the terminals, voltage went from12.54 to 13.1 over about a day. Now, two days later having been back on store again, the battery tested at 12.5v and lights are flickering on store (1st time ever). On store this morning, batteries show 12.2v (and lights again dimmed, flickering). I am guessing I've reached the end of the batteries, but thought that in store mode the 12v circuit would operate through the converter's shore power? Any insights or similar symptoms that would shed light? We're traveling full time; replacing converter myself seems a bit (maybe several bits) beyond my comfort zone. Figured I'd switch out anyway when the batteries gave out, but wondering what exactly is going on. Any RV service recommendations in the Knoxville TN, Asheville, NC area to have work done?

Thanks for what I know will be good advice (and comismeration), Al & Robin