I have a 373 JP Sterling and I have the same problem. I think it is a fact common to all baritones due to the narrower and twisted tubes than the euphoniums.It is enough to empty the water often whit the appropriate keys; it is a annoyance, but get used to it.
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.