It's perfectly possible to play beautiful lower register on a high baffle piece. However, if it's not working for you, then -- assuming you're sure your horn is in good condition (a tiny leak anywhere on the instrument can interfere with the lower register) -- you ought to try out something else. If I were you, I'd take my horn to the local sax shop and try out as many different mouthpieces as possible. If you don't find something that helps, then the mouthpiece is not the problem.