I've got a Bb clarinet (german buffet e11), which plays well and appears to have the typical tuning issues clarinets have on different notes - except that my low E (and the corresponding B) is very sharp. Perhaps my searching skills are lacking, but the only information that comes up is either about the actual E-flat key (presumably on a bass clarinet) or people's low E being too flat. If I leave the bell hanging on by a sliver of cork and blow too hard, then the pitch is almost in tune with the rest of the instrument. Playing normally, even with the bell pulled out as much as possible, leaves the note painfully out of tune.
What, if anything, (I'm imagining aftermarket bells or maybe barrel extenders) can be done to lower the pitch of a low E?