I had terrible results on my BA with any mouthpiece that had a medium or small chamber. I have been able to use, Links, Long Shank Soloists, and Morgan Large Chambers.
I am currently using a Morgan 9EL which I really like.
As others above have posted, I also think that the Link STM 7 that you mentioned should work well.
I just noticed that your Selmer mouthpiece has a 'B' facing. I can't imagine that I could get enough air through one of those to play it at all either...
The two Soloists that I use are both refaced, one has a .095 tip, the other, .099.
Good luck.