30-30 and 32-40 are fine in the little Martini action. Geometry prevents the use of longer fatter cartridges in the action, There isn't enough clearance for the cartridge to enter the chamber and turn the corner.

In the small Martini the 357 Maximum is marginally able to chamber. Sometimes it will fit and in other actions it will not. Some grind the feed trough out to make it work, but that has been the cause of a number of block failures---after all the breech block is technically the locking lugs.

Sometimes you can get more room for the Maximum by lowering the feed position by lowering the web of the lever. That is the correct way to adjust feed position not welding the trigger and recutting it as some practice.

The other issue of course is the barrel tenon of the small martini is only 3/4". Too large a cartridge body will lead to a bulge in the chamber over the threads. I have had this happen to every single .225 Winchester I chambered for customers. They all were warned. They all said they were going load down. What's the point? If you are going to load down use the lesser cartridge.

5.56 x 50R good choice!