Thanks for the advice!!
You are right on the Pianica 32A It has the same shape and the soft rubber outer skirt that mine does. Looks like a good fit. I will do some searching around for one of those. I will give the no mouthpiece thing a try too. That could work with a vertical orientation.
Interestingly, mine are branded “Artist Ltd. Pianica” but are exactly the same. The case is the same blue and white scheme and are marked P-34