TubeNet

I'm looking for a new mouthpiece to try, but I want it to be as close to the Conn Helleburg as possible (same flat rim, same rim diameter, and same interior diameter) with the exception that it has more of a bowl shape than the funnel shape. In years past, I've tried the Doug Elliot and the R&S ones, but with limited success.

Neither had EXACTLY the 'same flat rim, same rim diameter, and same interior diameter' as the Conn Helleburg. These are the features of a mouthpiece that seem to fit well to my face and that I sound the best on. Are there any newer companies that might have something like this? Or perhaps any older companies that have some newer stuff?

Look at the charts at
http://www.ibowtie.com/tubampccharts.html
to see if interests you.

The size is not going to be as much of an issue as the flat rim. I don't know how many of these have the flatter rim. The Kelly lexan does have a flatter rim; I really like the Kelly 18 for similar reasons along with my Wick 1 I use on my Besson (a Helleberg style cup with a slightly more rounded rim than a true Helleberg) and use one exclusively on my sousaphone. But for it being lexan, it's the closest dimensionally that you are describing that I know of. The Wick 2L is only a shade smaller overall, and has a similar rim that's not flat, but not totally curved, either, with a good focused bowl and reasonable "bite" on the inside of the rim. I have no experience with the new stainless steel mouthpieces. I hope this helps.

You can get most of the "Loud Mouthpieces" with the SSH rim. An LM-6 or 7 is probably close to the Helleberg in diameter. Putting the SSH rim on it give you as close to an original Conn Helleberg rim as you are likely to find.

If you like mass, then I'd recommend the Tony Clements piece. Picture a bucket with a helleberg rim. I don't know how to contact Tony anymore since he sold his shop, but the mouthpiece would roughly be 170.