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There are 4 traditional "schools" of german mouthpieces: Cologne, Leipzig/Dresden, Bremen and Vienna. None of those mouthpieces had a funnel shaped cup. They were all bowl shaped and they matched the horns from the respective area. The "Cologne"(Monke for instance) style mouthpieces didn't work well with the Leipzig trumpets(Heckel).
The modern rotaries like the Kühn are designed with standard mouthpieces in mind. Because of the different bracing, you will not hear yourself the same as on an american trumpet. Rotaries also have a unique sound for the low middle and high registers. I would say, keep using what you have until you can define what YOU think should be different. I use the same mouthpiece for my piston and rotary horns.
A picc is ALWAYS trial and error. I do not think that there are any set rules that really apply. In my opinion, intonation is the first consideration, then the blow and last the sound!

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