that was plan A, but I can't find a .17HM2 barrel for under 500, except for some that are backordered for a while.
I'm aware of the cartridges - my understanding is that to convert .17hmr to .17hm2, the old chamber would have to be cut off entirely, a new chamber reamed, put on a lathe to re-size for breach fit, extractor slots cut, and grooves cut for set screws to secure to the action (CZ 457 receiver).
Either all that, or re-line a .22lr barrel for .17cal.
For all of that machine work from a quality machinist, you are looking at more than $500 in labor. You might be able to find someone to do it cheaper, but good luck with the results.
As for re-lining a 22lr barrel, you are still having to chop off the existing chamber, and do all the other things you'd have to do for a 17HMR conversion, since dimensionally the 22lr is obviously wider. Since the HM2 is closer to the .22 Stinger, it's possible there's enough meat at the throat to ream but highly unlikely you'd get the correct dimensions. All of this may not even be possible if you don't have enough length to do this before the taper.
What you could do is buy a barrel blank, which would save you a little $$$, and have it reamed and cut, which would save a little time and $$$ on the machining side, but not much.
IMO your cheapest option is to buy the $500 barrel and have it installed. It's already cut/reamed/contoured, and would just require removal and installation, which should be pretty cheap from a qualified individual.
The 10/22 project would be far cheaper and faster, and Num1FordFan has done several of these builds so he's a very solid resource for info.
In all of this, keep an eye out for the dingleberries who call themselves gunsmiths. There's a lot of armorers who fancy themselves as smiths but can't do any machine work.