I have two Model 36 - the snub and the 3" - both excellent J frames and I often CCW them. As far as +P . . . . well obviously from the posts you CAN use it or so many do evidently. dMy personal opinion is "why"? I can shoot either of my 36s all day long with standard 38 special (my reloads), BUT, not with the factory grips. I've changed both out to Pachmeyer (S)P?) combat grips which makes a world of difference.
But . . and again, it's a personal opinion . . . why go to +P when a standard 38 special will "get the job done"?. Yea, maybe it will handle a +P but then again, there are those that would stuff a 357 in one if it wouldn't lock up the cylinder.
I've never understood, and especially for those of us that reload, the need or desire to load "hotter" than recommended just to push the envelope and then use it in a firearm that the manufacturer intended for standard loads.
Again, as seen in the posts, you can do it and probably get away with it. But if you want to use stronger/hotter loads, then why not get a 357 snub - there are plenty of them out there to be had. I would not classify the Model 36 J frame as a "range gun" and in my experience with mine, at SD ranges, with standard 38 Special ammo I have no doubt that either of them would be adequate. And in fact, both of my 36s do an excellent job for critters and woods walking using my 38 Colt Short reloads with a 120 grain cast lead slug.
But again, just my humble thoughts . . . . .