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Recently I treated my Melton 46S to a full-scale overhaul and it came back in perfect condition.
In the process, I had an additional set of 5th and 6th valve slides made:

- one set provides the same length as an F-tuba´s 2nd and 1st valve, respectively.
This setup is what I´m used to and has been with me from the very beginning of my F-tuba experience.
- A second (brand new) set of slides is longer and will provide a C-Tuba´s 2nd and 1st valve lengths, to go with an activated 4th valve.

The former setup provides the following advantage:
As you descend chromatically down from F to F1, the fingering scheme of the right hand remains the same as with a compensating system,
with some pitch tendencies.
"sharp" and "flat" means: manageable to lip to pitch, with concentration.
"all right" means: deviation noticeable, but easy to lip to pitch.
"perfect" means: deviation is smaller than, say, 10 cents, which is within my personal embouchure variability when looking at a tuner.

4 (perfect)
4-2 (sharp)
4-1(5) (flat)
4-12(5) (perfect)
4-23(5) or (6) (both all right at opposing ends of the spectrum)
4-13(6) (perfect)
4-123(56) (perfect)

The new setup SHOULD provide perfect pitches with different fingering patterns, because for each note one can come up with a fingering in the "perfect" category. The downside is that these new valve combinations are hard to enter into "muscle memory" and therefore lacks fluidity.

However, I find the pitches with this new setup running all over the place, and inconsistently so.
(That means: two consecutive notes, played on the same valve combination, might deviate 20-30 cents from each other).

Maybe I´ll just have to re-wire the connection between brain and embouchure if I want to get this to work.
Or just stick with the former setup until I might want to sell the horn to somebody who´s hard-wired to the new one...

That is a really interesting approach. Reminds me of a five-valve Bb horn, which has the Bb stop valve plus the fourth valve (pinky) that puts the bugle into F. On the horn though, that F extension is used only for the "missing notes" in the low range on the Bb horn, and everything down there is very lippable. It's used but not that much. You've just moved the whole thing down a fourth. As to why the pitches are all over the place, my only comment is that when I get a new instrument, that happens to me as I'm trying to set the valve slides. It's just all over the place, and somehow over time it starts to work and I have no idea why. Happened when I got the NStar back, and the CC is still migrating over time.

What you've had done sounds like a whole bunch of fun.
As I have "stuff" laying around here, I've had fun (most of them: temporary) making alternate slides for some of my instruments, and well as experimenting with pitching my instruments in different overall lengths (ex: C - B-natural / B-flat - A), and then trying out some commonly-played passages and excerpts with those instruments set up with half-step longer open bugles.

For over four decades, F tuba has been my "strongest" tuba.
I play it the best, and I sightread best using my F instrument.

It's a classic 4+2 set-up (nothing special, to those familiar with this set-up).

5 and 6 work just like 1 and 2, except they offer in-tune whole-tones and semitones, but with the 4th valve (perfect 4th) depressed.

I believe the one of the key secrets to an easily workable F tuba is a second space open C which is NOT sharp (as this pitch NOT being sharp seems to be a fairly rare characteristic with [most?] models of F tubas).

Working the two left-hand rotors with the left hand is not only logical/comfortable while offering mirror fingering patterns, but it also leaves the right hand thumb available (if needed/desired) for a #1 slide trigger and the left hand thumb available (if needed/desired) for a 5th slide trigger.

The F tuba "low range" is several steps higher than with contrabass tubas, which defines that intonation of those pitches be absolutely dialed in (as - over the last two or three decades - 1st-world humans have become much more accustomed to really dialed-in intonation in regards to both recorded and live music. If anyone is skeptical of this, pay attention to the intonation on some of the old sitcoms' themes and incidental music, vintage pop/rock band intonation, and several decades old classical music recordings on youtube. Much of all of that music is remarkably fine/virtually perfect, but a great deal of it is not...and that which wasn't was never berated.)