Playing on the flat side may be a common thing with JP horns: I bought a used (but practically new) 373 JP Packer baritone a few years ago: it sounded flat, not just the overall pitch, but also by operating the individual pistons. I cut all the slides, 1st, 3rd and main by about 15mm and the 2nd by 5mm per leg. Now it sounds perfectly in tune with the exception of the Eb and Ab which are slightly flat due to the length of the compensating tube of the 2nd piston which is too long (in my opinion). I also like the sound, projection and ease of response. I use a modified K&G 4B mouthpiece myself: deeper and wider cup which I alternate with a modified K&G T4C and SM4M. To gain something you can thin the outside of the shank of the mouthpiece so that it penetrates deeper into the receiver ( there is absolutely nothing to cut here). The operation is quite simple (you need a drill, a vice and some abrasive paper or cloth): the gain is not much, but it could be enough.
2007 Besson Prestige 2052, 3D+ K&G mouthpiece; JP373 baritone, 4B modified K&G mouthpiece; Bach 42GO trombone, T4C K&G mouthpiece; 1973 Besson New Standard 3 compensated valves, 3D+ K&G modified mouthpiece; Wessex French C tuba, 3D+ K&G modified mouthpiece.