I really love my metal Berg Larsen 120/1M for Funk, Rock, R&B bari sax. It's also pretty good for a nice powerful contemporary big band sound. I don't know about the beechler bellite mouthpieces for bari, but for alto they were pretty open with a fairly low baffle and didn't really have that contemporary commercial edge I needed for my current pop gig. There might be other suggestions from some of the other bari players, but the Berg is pretty much a standard for modern bari. Doc Kupka from Tower of Power plays one, if that's the type of sound you're looking for.
With that said, if you already own the Beechler I don't think it would sound bad, they're pretty great sounding mouthpieces. I think you'd be fine on it, but if you're looking to buy a new one my money's on the Berg or maybe try out a Jody Jazz if you've got the cash. The woodwind & brasswind will let you order three mouthpieces at a time to trial, just send back the ones you don't want and they give you a full refund, minus the shipping. Or if your local music store has them and will let you play them, that's always the best option.