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As far as I'm concerned, there are no secrets. Just know all your scales really well, and start doing it as often as possible.

Having accomplished this, I can only reiterate what the above poster said: Have your scales absolutely locked in!

When in the military, I played BBb (sousa) for marching band and most often played CC in concert band and brass quintet. I found that the more I refined my scales, and the more that I played BBb and CC, the less difference it made.

At one point, when my Army band bought an F-tuba, I decided to try to get to the point that I "owned" F-tuba fingerings by playing F-tuba for everything except the marching sousa gigs for an entire year. It was a long year, but 25 years later I can sit down with an F-tuba and am OK with it within a few minutes.

I'm 69 years old. The older I get... the more I struggle with 'switching back and forth' between BBb and Eb. Ten years ago switching was second nature and I would be 'locked in' after just a couple of measures. These days it takes half a tune and I really have to think about the fingerings. I took a little Eb to Shrine Band practice tonight and it was a struggle. The eyesight is going too.

Enjoy it while you can!

Switching between CC, F and BBb has gotten easier since i switched to a rotary F. At one point my F and CC were both 4 piston 1 rotor and the sousaphone i was using was 4 pistons (Jupiter 590) they we so similar to each other it was difficult to keep all 3 seperated.

I often do the same thing, my wife just ignores it but the folks I work with are always amused when I start moving my fingers in strange patterns during boring meetings.

I have a similar situation to the OP in that I also have a Alex 164 BBb, and other horns in CC. For me, I learned to play on CC and had no prior BBb experience before I got the Alex. I spent a solid 3 weeks trying to work out my next concert program on the BBb, including taking the horn to a rehearsal, but that particular program had a lot of challenging pieces with lots of moving notes and accidentals, so I decided to give up and play the program on my 163CC.

I love the sound of the bigger horn, and there's a part of me that says just find a way to get one in CC. But then again, there's something to be said about having the versatility to be able to play a BBb horn when the need arises. Plus, there are an awful lot of band pieces that play more comfortably on a BBb (Stars and Stripes Forever being the first example that comes to mind). My process for learning the BBb has been kind of a hybrid of reading the more common notes at sight (e.g. B-flats and F-naturals are open) and then "transposing" the less common notes up a step (see a G-sharp but finger it like an A-sharp). The more time I spend with it, the fewer notes I have to "transpose" in my mind. I know some people prefer to use an "immersion" method where they will only use the unfamiliar horn (BBb in my case) for everything over a period of months or longer. For me that's not so practical because the 164 is a beast and would really be a pain to take everywhere. One interesting side observation that I have noticed is that after playing the 164 for any appreciable amount of time, I pick up the 163 and it feels much easier to play. If nothing else, that 164 makes for a great training tool for improving air capacity and projection.

So I remain a bit conflicted - I really need all the practice time I can spare just to keep up my CC playing. On the other hand, working on new things is one way to keep the brain stimulated - I probably need that more...

Everyones different.
I started on BBb at 12 and was learning CC already at 14 and F at 16. (Never got to Eb. Real pity. Did play some D helicon in a band for a while, which was a too low pitched Eb with some slides pulled and probably an inappropriate mpc).
After Conservatorium I pretty much gave up on trying to fit into the orchestra-studio-musical-avant garde-"legit" world and have made my $$ almost exclusively with pop music, supplemented with jazz, world, etc. And nowadays, ya, brass quintet, studio, musical, whatever gigs. You never know where you end up in life.

(pause to emphasize that last statement)

At some point I stopped playing CC and sold them all. In hind site it was't maybe the most brilliant move but at the time I just couldn't/wouldn't/didn't work improvising on both Bb trombone and a CC tuba. It just didn't fit in my brain.

As you can see from your post, everybody has their own story and own way of making it work, so...
make it work. If you can work BBb and CC (regardless of the size or model) do it! It'll only benefit you. If it becomes a burden you'll stop with one of them anyway. In the meanwhile it is to your advantage to play both, at least until the day you find a tuba that responds almost identically to it's "other-keyed" counterpart.
But if that day will ever come......?

With the caveat that I've only owned a CC for about 4 months in the last 25 years, it wasn't a problem for me.
I bought a Miraclone from bloke, played it on 3 gigs in the first 2 weeks, and was fine with it. I pulled out etude books and just read for a couple hours to get the fingers back.

No issues, aside from figuring out how to tune the 5th valve, my preference was a little odd (now, I don't even remember what it turned out to be) but it was very comfortable, even moving from the long whole step on my F. Going back and forth to BBb was frequent in my practice sessions, because I wanted to develop that fluency.

But, I do the same with F and Eb. I rarely have a problem. Maybe I'm just lucky, maybe it's not as hard as some make it out to be. I dunno. It works fine, though.

The danger for me with switching from Bb to CC occurs when there are long rests in orchestra, and my concentration fails. If all of a sudden I realize I have to go back playing but I was miles away with my thoughts it can happen that for a scaring fraction of second I think "what am I playing?" Then, as long as I keep playing everything is easier. Also, if the instruments are very different in size, weight and ergonomics it's much easier for me to switch.

Try playing four or five different tubas in two to four different keys each day. On community band night I scramble home and jump in the shower to scrub the buffing compound off me. I get dressed in clean clothes and dash off to community band. I get there not early enough so that while I am still setting up, the band director starts conducting to prove his point that everyone should be on time or early like his retired arse that's enjoyed a long nap that afternoon. "Oh crap. I've played everything but F tuba today. Think F tuba, F tuba, F tuba." Then I start to play. Then I start to wonder, "Why do I bother with all these different key tubas at home? I should just sell everything and play my old 3 valve King as that sounds good enough for these groups. No matter what key or size of tuba I use, or the fact that I play two dynamic levels below what is written, the conductor always complains we're too loud." Ah screw it. I'm a tuba junky and I like my different tubas!

Very glad to hear that I am not the only person who does that "finger-samba" !
Maybe I am not at last so strange while some tend to think so...