Here's an update. I figured I'd rather put it here than face the guffaws of the actual gunsmiths in the gunsmithing section.
I ordered a .22 Magnum cylinder reamer from 4D Reamers in Kalispell, MT. 34 bucks plus shipping. The rental is for 7 days, but they give you 17 days from when it is shipped to cover transit time. (Doyle is compelled to sit on all new mail.)
There is no handle, just the reamer. I bought a cheapo tap handle from Tractor Supply (8 bucks) but it wouldn't tighten enough to hold the reamer securely. I bought a slightly better one from Lowes that tightened like a drill chuck (15 bucks) and it worked fine. The cutting oil (4 bucks) from Tractor Supply was good.
Then I sat down, poured a glass, put War Horse on, and started twisting (over a trash can).
Initially I wrapped the cylinder with blue painter's tape, but the oil got on it and the tape just turned. I used a cloth and a good grip and started making progress.
It didn't seem like I was getting anywhere at first, but I took the reamer out often, sprayed it off with WD40, drenched it in oil, and before long the first chamber was done. The whole thing was done before War Horse was over.
Mixed bag of .22 WMRs chambered fine. At the range I had a hard time with the cylinder not wanting to close and being hard to cycle. Turns out some of the metal chips got under the ejector star. Once I blasted them out all was good. As as a bonus, .22 LRs and Shorts also shot and ejected just fine.
So there you have it. The forum friends who suggested the chambers were out-of-round were right, I think. When twisting the reamer there was a distinct "resistance/no resistance" feel. They are sure round now.
Thanks to all who chimed in. I hope this was helpful to someone.
Here is my dog Randy about to catch a ball, as a small bonus.
