Your first thought (JM stamped 336) is my suggestion.

Please don't saddle the kid with a backward rifle. If you want him to learn to shoot well he needs a gun that fits and runs with a whole lot of extra problems. LH bolt actions are easy to come by nowadays but then you run into the issue of length of pull.

The easy answer with kids is an AR. The controls are pretty much ambidextrous. I put ambi safeties on mine, but it's not necessary. The adjustable stock and light recoil work well for young shooters of varying sizes. That's what my kids use. One is very recoil shy, so she uses a .223. The other uses a 6.5 Grendel. If you don't already have an AR, this is a good excuse to get one.

The only downside we have found with hunting with ARs is that you need to tune the ejector and extractor on some to make chambering a round quiet enough. Otherwise, you want to load well away from where you are going to hunt so you can let it rack in there.

We do almost all their practicing with a 22lr AR since the gun is the same. I learned early in practice to keep the mag out of the gun to make it a single shot. That boy of mine will empty a mag in short order if he isn't forced to make every shot count. It worked. He's one shot one kill on deer.