BLUF: I would strip the reciever (10 mins tons of youtube vids) blow it off with brake cleaner and build up a rifle of your choice. This takes pretty basic tools to do. Easier than an AR build. I am a trigger snob, so my rifles have Timney, Jewell, or KiDD in them. I recommend a complete trigger ASSY for your KIDD because I am Texas biased, and KIDD is up there with Jewell in feel and break.
Well, so I will tell a little backstory on my 10/22 really quick...
I built a PLR rifle off a 700p back before I started reloading a few years back, and my wife decided she wanted to learn how to shoot. Rather than buy 1k rounds of .308 ammo and burning out the wife's shoulder, or my rifle's barrel life, I decided to build a sub moa capable .22. I had chosen the Ruger 10/22 platform because of simplicity, and the fact that I already knew about KIDD/cool guy guns out of Texas. I took an old 10/22 basically completely gutted out the reciever, cleaned and sold all the ruger parts. I built my rifle up from that with ALL KIDD parts excluding the stock. I cannot remember what it ran me back then for all parts, but I purchased a bolt, buffer, cocking assy, 20" bbl, single stage trigger(1lb). I pieced it all together in a Boyd's Tacticool stock, because that afforded the same ergonomics as my .308. Now, your looking about about $480 plush shipping for the parts, and I believe the stock runs about $100.
It was a perfect excuse to add another fine rifle to my collection AND teach the wife how to shoot without wear and tear on my bolt gun.
Pictured is my 308 and the trainer rifle on the range with some friends.