> 2-3
> 1-2-6
> 3-6
> 1-5
and (if needed to be way sharper) even
> 5-6
These options are not going to be immediately under the fingers of someone new to 6 valves, and they are never going to become completely automatic to longtime players of 6-valve instruments, but they're there, and are useful for dialing in 2-3, which is probably the most squirelly valve combination on all valved brass instruments - just as 5th position is the most squirrelly trombone slide position. (1-3 or 4 is even more squirrely, arguably, but only involves two pitches, so...)
Having dealt with tuning problems on a bunch of tubas, I've decided that mouthpieces that offer less (so-called "slotting") or (thinking of it in another way) offer MORE "tuning flexibility" are better choices for instruments with more tuning issues. I tend to also prefer smaller mouthpieces with smaller instruments as deep mouthpieces (particularly with larger throats) seem to tend to "overwhelm" smaller instruments - often resulting in a type of sound that - to my ears - is too "covered". As far as pitch"favoring/lipping" is concerned, our decades of experience also tell us that it sort of goes out the window at extreme volume levels, as well as extreme upper pitch levels (ie. "way up there"). F tubas - with E-flat/B-flat size mouthpipe tapers and E-flat/B-flat valveset bores - are sort-of enigmas, as far is "what types of mouthpieces are best" is concerned...at least, in my experience.
Your theory about "where a valveset is located in an instrument" is a good one - because it involves WHERE the tapered bugle is absurdly distorted by a bunch of cylindrical tubing, but the taper of the cylindrical tube itself (and you know this) is also a big factor. Those computer programs (which take all of this into account) never find perfect solutions (as there are none), but can offer less-bad ones. Working with instruments which were designed prior to these programs having been developed is going to involve ingenuity combined with luck and - as these programs are far from perfect - ingenuity is necessarily going to be involved in recently-designed - so-called "computer-designed" - models as well, if we are to completely "dial in" intonation when we are playing (as modern recordings - to which laymen are exposed DAILY, on TV, nearly always offer extraordinarily superb intonation -
so we workaday/not-Heifetz-level musicians are now expected to meet higher tuning standards than was Heifetz himself
) I clearly recall that very minor tuning issues (in the distant past) were met with just a little bit of nonchalance ...and none of this is meant to be rebuttals, but only agreements.
