A bike with only 300 miles on it should not need a valve adjustment no matter how long it's been sitting. I wouldn't bother with them until you have the carbs sorted out.
Take care of the simplest things first.
A couple things I didn't see mentioned (sorry if I just missed them);
There is another fuel filter located where the fuel tubing meets the carburetors. It's a tiny duck bill shaped thing that fits inside the "T" where the tubing slides on.
You only seem to be experiencing a problem with one carburetor, so sort that one out first. Clean the jets with a tiny piece of wire and shine a light through them to ensure that there aren't any obstructions. To find out if the diaphram is the problem, try swapping it with one from another carb and see if the symptoms move to the other cylinder.
Some carb problems turn out to be electrical.
Doubtful at such a low mileage, but a bad coil will cause stumbling at low RPM and a fouled plug. Hang the plug wire of the offending cylinder off the side of the bike and attach a grounded spare plug to it. Make sure you're getting a nice fat consistent spark. If not, do a search on here for coil problems.
...just remembered one other thing about bikes that have sat for a long time.....check for mice nests in the airbox!
