It sounds as though you recognize the need for some embouchure development independent of how any given horn plays. It also sounds as though perhaps you haven't been playing very much for a while and need to get back in the groove.
You DEFINITELY shouldn't be cutting any horn (especially one of that quality) without KNOWING that its pitch is incorrect. I'm shocked that a repairman suggested this.
So yes, start playing regularly (daily) and see how things change. I don't think it should take months. More like weeks to see a real difference.
Another thing you can do is to have another euphonium player play the instrument and see what he/she thinks. This should be someone you know is competent and experienced. That will tell you right away whether it's the horn or its you.
There is no "close enough" to being perfectly in tune (though this doesn't necessarily mean "in tune with a tuner" when you're playing with an ensemble). However, for practical purposes, if I'm more than a couple of cents out in one direction or another, I'm not happy. I think I read somewhere that the human ear can detect a tonal variation of 3 cents. Anybody else know if that's correct?
Gary Merrill
Wessex EEb Bass tuba (DW 3XL or 2XL)
Mack Brass Compensating Euph (DE N106, Euph J, J9 euph)
Amati Oval Euph (DE 104, Euph J, J6 euph)
1924 Buescher 3-valve Eb tuba (with std US receiver), Kelly 25
Schiller American Heritage 7B clone bass trombone (DE LB K/K10/112/14 Lexan, Brass Ark MV50R)
1947 Olds "Standard" trombone (Olds #3)