Well....I think I have it figured out. On top of the Charger/Inverter box are four RJ-11 plugs. One is labeled "Remote." If I disconnect that plug, the meter goes out/turns off. Hence pulling that plug should eliminate the parasitic drain. It's a bit awkward to do that...but it should work.
I guess the logic of having the meter powered full time is this: The remote unit allows one to program various events to automatically start the genset. For example, some folks set it to a particular time or temperature so that the dog or grandma don't get too hot 'cause the AC will come on.
Oh, well....our dog died long ago....and grandma (usually) goes home with me.