You're right, a lot of crud can get in there, and I'm probably overdue to remove my grips for a thorough cleaning. The part I hate is putting them back on, and trying to keep the mainspring strut in the little pocket while I'm doing it.
Speaking of which, I put a Wolff reduced power mainspring in my 4013TSW a few years ago, and it really improved the DA trigger. The factory spring is about 20lbs, and I believe I put in a 17lb spring, which was at the time the factory weight for the DA-only pistols. You might give that a try to lighten the DA trigger. Just do a good amount of range shooting with it to make sure you don't get light primer strikes before you carry it.