Adjustment screw on Walbro LMT...

I would guess it's for idle mixture. If that is the case maybe backing it out that far is compensating for a partly plugged main jet. Just a guess but sounds like something might be getting plugged somewhere especially if it still does not run all that great with that screw backed out.

You can get a manual here if you need one:

Manuals | Customer Support | Briggs & Stratton

Unfortunately it does not show carb adjustments (what little can be made) in it.

It actually does run pretty good backed that far out, but I know there has to be a reason for it. I know when I cleaned the carb a year or two ago, the bottom of the bowl was a bit rusted. I cleaned it good, but maybe a chunk came off since. I think I'll pull the carb one more time and spray/blow through the passages again and put a new bowl on it.

First, a new air filter and plug. I doubt that will make a difference, but those haven't been replaced since I got this mower from 'a butcher', so it can't hurt.

Thanks for the info and link!
Pat