Couger.
Sorry I have no knowledge of the Hornet barrels sizes. I had a look at a Hornet Handi rifle once and it had a very flimsy barrel, nothing that I would have rebored. But I only saw one. A toy like rifle with a plastic stock.
For myself the 223 24" bull barrel is the only one I would consider. Also a 22" 223 could be used. The 26" 26-06 for bigger calibers is good too.
The way my two converted rifles balance has to be felt to believe. Of course the octagon barrel treatment and the lighten of the stock moves and shifts weight between the hands.
.221 FB .22 BR and 6mm BR, non of these can be used with an existing 223 chamber. A 22 Hornet chamber would be usable for these.
Of course you could bave a barrel stubbed in any caliber you want, but in my opinion this is not at all economical when you consider the intrinsic quality of the H&R action,
unless you can do all the machine work yourself.
If you are a wildcatter you can do all sorts of case shapes with a 30-30, for a volume of 34 to 44 grs. A 1.800 length would work well..
Or the 225 Win. A shortened 220 SWift. Possibilities are endless for the 6mm and the 25.
For the equivalent of the 6ppc the 6x47 is a fine substitude with the same volume and power. Besides this is a simple wildcat and well suited for a beginner wildcatter.