Hey Keith,
If you're going to leave it a 222 Rem, I wouldn't go any shorter on the barrel than 12". Doubt you'll get much performance shorter than that.
If you do decide to rechamber, will you stay rimless or consider going rimmed?
Rimless: 222 Imp, 222 Lynx, 222 Mag, 222 Mag Imp, 223, 223 Imp.
Rimmed: 222R, 224DA,
225 Win, 226JDJ.
There might be others I didn't think of.
The longer the barrel length on all of these the better IMO.
Naturally I'd go with the 222 Lynx, 224DA or 226JDJ (just because I'm a "wild" kind of guy).
Larry