Okay, here is how you look up things that are comparable to what you have. In your case, I went to
http://www.dwerden.com/mouthpieces/tuba.cfm and selected one of the mouthpieces you liked and clicked on the Miraphone 31 at "Rim / Inches" and came up with this list of mouthpieces, many of them showing the bore diameter for comparison -
http://www.dwerden.com/mouthpieces/tuba ... pare=33.00 . You can see that there are a lot of mouthpieces with that inner cup rim size and bores from 7.4mm to 9mm. Notice the Josef Klier mouthpieces and how they are listed. They have gradually shallower cups as you go down the alphabet with the bore sizes adjusted for cup depth but the inner rim size
ALWAYS stays the same. Your PT 50 shows up on this list, too. You don't have to mess with re-boring mouthpieces to experiment with the throat size for a given rim. Whatever bore you would like is probably already available. There are some pretty pedestrian mouthpieces on the list, Like Bach 7 and 12 and The Klier T3 series (AA is the deepest, E the most shallow).
Experimenting with mouthpieces is fun and a well equipped shop will have a lot of them for you to try. But, try to lock on to one you like and one that works for you and stick with it for a few months until you have proven it out, one way or another.
Always make a good sound; audiences will forget if you miss a note but making a good sound will get you the next job.