Today I made with the stripping and reassembly of the Mk.III 22/45; it was nowhere near as annoying as I feared, although I don't believe I'll be making a habit of stripping the bolt.
For what it's worth, this is the first time it's had more than a bore snake run through it since I bought it. The earlier Ruger rimfire autos were remarkably tolerant of filth, and I was curious to see if the extra mechanical gizmos in the Mk.III action would cause it to get befouled by cack quicker than its progenitors. Despite having enough fouling in the action to support the planting of row crops, it kept running with no real care other than occasionally squirting some Strike-Hold in through the ejection port.
On Shannon's recommendation, I installed a Power Custom extractor.
The trigger is still heinous.