The sleeve insert is an OK idea.
With a 35K psi caliber in there, I'd want at least a reduced size firing pin (bushed firing pin) and better one that has some way of venting off the gas should a primer or case give out.
It doesn't say wether such was done in the conversion. I'm guessing not.
If a case does fail, even a small case like the 357 can blow back through the action and destroy the stock and do some real damage to your face and hand. Especially being on that side for a right handed shooter.
The Nitro Specials just use a short rather flimsy firing pin held in place with a small dia set screw. That'd probably sheer off and become blow back debris should such a thing happen.