I have a current-issue Selmer Soloist alto mouthpiece (bought new a few years ago) and Selmer scroll-shank soprano mouthpiece (not marked Soloist but...
I'd change mouthpieces before I changed horns, a lot cheaper that way. All horns vary to some degree, so when I tell you my VI or TH&C or Big B or TT...
I purposefully did not comment on the horn-protection issues because the OP just asked about which gig bag to use, not about if it was a wise choice....