After a year of searching, I finally found a .22 Hornet (that I could afford). It's a lowly H&R Topper, but I stumbled on to it at a fair price locally. It came with a Simmons .22 rimfire scope, which I used for the first range testing. I've since put a Bushnell Banner 4-12x on it for load development.
Good news: With Hornady factory ammo, it shot at under a 1/2" at 50 yards and about 3/4" at 75 yards. And that's with what must be a 12-pound trigger pull.
Next step is getting dies and finding some cast loads for it. I've got the Lee 55 grain flat-point mold that shoots well in my Triple-Deuce, but it may be too heavy for the Hornet.
Red Dot is pretty much the only appropriate powder I have on hand. I've got a bunch of 4227, but I'll have to research that.