What Der Ami & Waterman said plus these thoughts:
If the rifle is set up to feed the .22-3000 Lovell from the magazine getting it to feed the .222 Remington reliably may not be an easy task.
As Waterman said, a factory loaded .222 Remington is probably exceeding the safety of the 1922 M1 & M2 design. I've seen lots of G&H conversions of M70 Hornets to .222 Remington but I can't recall seeing any G&H conversions of M1 or M2 1922 Springfield rifles to .222 Remington although G&H used to advertise that the conversion was available for "suitable rifles".
You could rechamber to .222 Remington & reduce the load for lower pressure but you would still be handloading so what is the point. Proper dies & bullets for the .22- 3000 are available & if you look hard enough you can still find new G&H .22-3000 cases for sale.
Rechambering that gun to .222 Remington because you don't want to reload is like replacing the V12 engine in a vintage Ferrari with a Ford V8 because you don't want to deal with the expense of maintaining a Ferrari V12. At least in the case of the Ferrari it would be easier to reverse the alteration.
