The model 357 is the closest to the Python. I've shot one or two with truly wonderful actions and Python-quality accuracy. They're nearly as over-priced as Pythons these days, but if you look long and hard enough, you can probably find a bargain.
The Mark III isn't a Python. Mark IIIs are good shooters, and I sincerely wish I had the one I bought in the late 1970s, but they're a notch down from Pythons.
Most people are perfectly content with good Smith & Wesson revolvers made before the start of this century, which are widely available, often affordable, and can be tweaked to deliver crisp, light, consistent trigger pulls. What's the secret? A gunsmith who knows what he's about. There's no substitute.
It may be worth bearing in mind many shooters think they can tell one reasonably good trigger from another, but actually can't. Unless you've been spoiled by a phenomenal trigger, you can get by without a good Python trigger pretty well. It's definitely worth bearing in mind not all Pythons left the factory with good triggers, and many good triggers can be improved. The secret? Again, a top quality gunsmith. The problem? Finding one. Contrary to what many gunsmiths will tell you, the good ones are few and far between, and they tend to charge accordingly.
I swear by my Pythons; I'll also admit gun snobbery can be expensive and somewhat silly.