The order of the mouthpieces seem to have been mixed up
Hammond large shank mouthpieces go from M, ML to L and XL. Small shanks can be XS, S, M, ML. Now the Hammond site says L is only large shank but I have both 12L and 13L small shank and even a 12XL small shank. Maybe the deeper small shank mouthpieces were not that popular so they were removed from the list. The MXL is a special order and is a modified ML cup. 12 is close to a Bach 5. The large M has the most shallow large shank cup and the XL has the deepest cup and that one is intended for euphonium. After a lot of experiments I've found the 12 is the best match for me.
I have experimented with 11M, 11ML and 11L too. I have never played a 11MXL but in allegory with the others a 11MXL is a modified 11ML. Size 11 makes me tired. It's too wide rim for my taste. The 11 is close to a Bach 4. You need a very strong emboshure to use a 11L on a heavy first part. I would not do that.
All Hammond mouthpieces have comfortable rims. I could use a 11L on a 2:nd or 3:rd in a ten part brass ensamble, 2:nd in a symphony orchestra on heavy work where you need a strong bottom or a 4:th part if you need to cover a bass trombone part with your lagre bore tenor and need more power down there.
Of course you could use a 11L for solo work too. It could help to produce an dark sound in the whole register, with a good bottom. If you are very strong you can make colors in the high register too, but it takes heavy work. I think a bigger chance with a mouthpiece like that is the sound becomes unfocused and euphonium-like and makes you tired.
/Tom