I know you didn't ask me, but while we wait for a good response I'll offer up a bit of experience from my world of making stupid custom mouthpieces.
A lot of the difference that you experience from different instruments is completely the difference in leadpipe. It's often assumed that there is some relationship between shank size and bore, but this is completely false. The difference between the old Conn Euphoniums (ex: 20I) and the ones with the Connstellation leadpipe (ex: 24I) is pretty noticeable. The new leadpipe has a larger bore and produces a bigger, less focused sound which seems more modern (to me). This difference is maintained with whatever mouthpiece or adapter arrangement I'm using. The original Conn 5 mouthpiece has a backbore so tiny that is practically is a small shank mouthpiece. Still, the horn sounds different from the ones with the older leadpipe.
So we get to the mouthpieces. If we make the mouthpiece longer without changing the backbore, then the shank size increases without actually changing anything. An adapter that does what it's supposed to should use this principle. Quite a few mouthpieces are just doing this, one way or another, so they shouldn't sound any different. What will make the mouthpiece sound different is changing the angle of the backbore. Technically, larger shank sizes should have the most advantage because they have the most room to adjust the backbore length, and the most room to use larger throat sizes. Concerning the throat size, this point is completely moot. Josef Klier can fit a small shank mouthpiece with a 7.6mm throat.
So what can we do by changing backbore length? Uhh...I haven't gotten around to testing that on Euphonium yet. Sorry. It is at least somewhat known and tested on other instruments, but there's no intuitive way that I can describe it. Furthermore, unless you are ordering custom mouthpieces, you are limited by what is available.
Hobbyist. Collector. Oval rotary guy. Unpaid shill for Josef Klier mouthpieces.