I owned the Sig .22lr conversion for a P220. Reliability was very good after a break in period. It shot just about any 40 grain ammo. Some of the lighter bulk stuff didn't have enough recoil to cycle it. It shot Stingers very well. It was more accurate than my Kadet, but the Kadet cycles virtually any ammo.
By comparison my Mark II is as accurate or more than the Sig, and is as reliable as the Kadet.
I would recommend the Sig .22 as conversion for those who own a P220/226, but it might not be the best choice as a stand alone .22.
One of the more accurate .22's I shot this year was a friend's Kimber conversion on top of an inexpensive Springer Mil Spec frame.
How about a Volquartsen upper
, red dot sight and a trigger job for your Mark III.