I have a decent amount of 357 Mag guns already and have a load that I run through them all.
The load is a 158gr XTP over 17g of H110.  This is the published Max load when I bought most of my guns but has since been reduced to 16.7gr in Hodgdon's latest manual.  I load them by the hundreds and like to keep one main load in stock.  The 0.3gr makes a decent enough velocity difference to not want to reduce my hunting loads.
I run it through my Ruger SP101, Ruger GP100, Ruger 77/357, and Marlin 1894.

Would an Uberti Single Action hold up to this?  Are any of the Uberti models known to be more durable than others?

I would not put max loads thru a Uberti SAA.  Well, not many, anyway.  

The original Colt Single Action Army was chambered in .357 Mag after it became popular.

That little hole in that big cylinder can take a lot of pressure even if it's not the best steel made.  

I wouldn't think the Uberti would have any problem handling those loads.

I would only be concerned about it losing time, or flame cutting on the frame.  Just watch the frame, and the rest can be fixed if needed.  

Or, there is another choice..................

I agree with the above.  As mentioned, the small diameter of the .357 leaves a lot of meat in the cylinder.  I wouldn't be concerned if it were mine but it's your call.

I can't help but wonder why shooters automatically think Uberti's won't hold up.

Here's a thread in which this notion is dispelled.

 If you don't want to read the entire thread, here's all you need to know-

  C.I.P. is Europe's version of SAAMI and they set the chamber pressure standards produced by firearms manufacturers who are members of the organization, which includes Uberti. The maximum average chamber pressure they have set for the .357 Magnum is 3000 bar which converts to about 43,500 psi. (SAAMI sets the maximum at 35,000 psi for domestic ammunition) Additionally, all firearms produced by C.I.P. member companies are required to be proofed with loads generating chamber pressures 1.3x the maximum average pressure. So, not only are all Uberti .357's rated for 43,500 psi, they are proofed at over 56,000 psi. As such, Uberti's are capable of easily handling any domestically loaded .357 ammunition.

Bottom line, shoot any .357 ammunition you want, and don't worry.