Remember Deadeye's 307Win Handi? Seems like you could cut a rim on a 7mm-08 chamber and use 307 brass.
If you want 7x57 or 7x64, just watch eBay and the classifieds here until a factory 24" barrel or gun comes up for sale. They made them up until 2001 or 2002.
On the hot 22 issue, how about a 22-30-30 or .225Win if you want a rim, or 222 Rem Mag? (although a factory 24" 22-250 ultra sounds easier)
When I first started looking at H&R/NEF, I thought about buying a hornet and rechambering it to 22PPC or 22BR, but decided that was pointless.