Sounds like a good question for Seewin, 3dub, or Bert. I think you are on the right track, since .22 long rifle ammo is far easier to find and cheaper, but if you wanted to keep it in .22 short, you can likely find a .22 short carrier for it. The M1906 and M62 could handle all three, and I think a carrier for either might work also.
Best of luck with it.

 

I got a 62 as well as a Rossi 62 SAC they both have a 3 ammo carrier all you would need is the Carrier that handles all three cartridges then you could shoot all three S/L/and LR, you might be able to find one at Original and Reproduction Firearm Gun Parts Winchester, HOMESTEAD GUN PARTS, Specializing in Old Winchester
today you can find a 22 LR that duplicates 22 short velocity or even 22 CBs
So your not short changed (pardon the pun)

 

It appears that a previous owner has put a chamber reamer into the chamber to lengthen it so a 22 Long Rifle cartridge will chamber in the rifle. Similarly, the carrier has either been altered or replaced so that the rifle will function with 22 LR ammunition. I have seen many rifles altered like this. However, those alterations do nothing to the twist rate of the barrel, which is intended for the lighter 22 Short bullet. This means that even if a 22 LR will fit, it seldom gives acceptable accuracy in a 22 Short barrel. Functional? Yes. Optimal? Not really.

Were the rifle mine, I would buy a 22 Short carrier, and install it on the rifle. They are almost always there to be found on eBay. Decent accuracy can often be had even with a pitted bore, as long as there is decent rifling.

All the best---

BRP

 

The carrier you have looks to me that it was designed for 22 Long . the history of many of these rifles were gallery rifles and many have mismatched parts this could be one of those. I have spare 22 short carrier in my parts bin I''ll look for it and check dimensions. the ideal carrier IMO is the adjustable one takes three sizes of .22s