I know this will sound way weird, but I had a used (eBay) system that had a varying barometer similar to what is being discussed.
Drove me nuts, constantly fiddling with the displays, etc.
I had a battery failure, and after I replaced the dry cell (heavy little sucker) I'm running higher voltage readings on the diagnostics, and the barometer is tracking exceptionally close, with a few hundredths of an inch most of the time. I don't know if I reseated something when I opened to box, or the lower than expected, but still functional for most of the other systems, helped. Might be worth a try to see what the voltage is, if not 6+ or slightly more.
Remember this is NOT NOT NOT a 12v. system and innards have been fried when someone hooks up a 12 supply to see if all problems are due to bad battery.