I suspect that neither the casings nor the pistons are up to snuff.
I would recommend having Dan Oberloh (out in Seattle) hone your valve casings to perfect cylinders (more "perfect" than the factory's definition of "perfect") and then stripping the nickel from the pistons, "starting over" (with the same pistons) and fitting them to the casings to the best (maybe even better than the best manufactured) standards.
If you would also like the slides perfectly aligned, he would probably do that prior to rebuilding the casings and pistons, because non-parallel and skew slides will bind, and put undue stress on valve casings (which is why I'm encouraging you to ALSO have the slides scrutinized).
Since your valves probably aren't "worn" (but just modern-age C-S mediocre), they probably will end up only barely larger than o.e.m. diameter.
If your pistons are typical (and you examine them really closely in good light with really good reading glasses), I'd predict that their surfaces are "grainy"...and they're really not supposed to be...but grainy surfaces is only one issue...as other issues are imperfect cylinders (pistons and casings)...along with (again) possible out-of-alignment slide stressing on the casing ports.
Again, if you unbolt the valveset and only send that, those detachable braces might also be under a bit of stress, and bolting it back on (when you get it back) could define (ugh) sticking valves...so I would send the entire instrument (even though that's really costly, these days)
Although these are small details, I might also recommend venting (at least) the #1 piston (but venting the rest promotes nicer slurring) and replacing the metal guides with synthetic.
If I really liked the way that a King 2341 plays (and I have a lot of respect for how they play - and one of my personal instruments is only a bit different - similar but maybe 1/8th smaller), I'd consider upgrading it from a school tuba to a personal/professional-grade tuba.
Here's my Holton (19" bell, only 32" tall), and with a 5th valve to help out the low range, but (more than that) to give me a perfect alternative to 2-4.
Yes...It's a B-flat tuba, and the valveset was (heavily altered and) taken from a (pre-Conn-Selmer era) King:
...and yes, my "'work-around" (avoiding a complete rebuild, as my pistons were (nope: not sticking) but very slightly loose-ish, was to notice that a used/for-sale set of MAW pistons was/were barely too tight in my casings, so lapping them into these casings defined closer tolerances...but that's probably not always (if very seldom) the case...ie. I was stupid-lucky in this regard...BUT I did have to obtain those pistons (ie. $$$).