I think I improved fairly quickly at speed, and even though I'm not some kind of stream g0d, I stream / burst pretty much equally well on all BPMs. My singletapping is way faster and better than my 1/4 speed, though. (270-280ish)
It's hard to pin down the exact things that made you improve, but I did focus on speed quite a lot because I had certain maps I wanted to beat that required 240BPM singletapping and bursts.
The way I did it was to create a collection with high BPM maps around my range that weren't too demanding in terms of finger control, and play certain maps and most of their diffs several times throughout the day.
The maps I felt were the most helpful (and thus played a lot) were Kokou no Sousei 4* and 5* (both 3+x a day) and a lot of other Yousei Teikoku maps (Mesorogiwi, The Creator, Sacrifice, Asgard, Hades: The rise yadayada), 500 Tortures 4* which I felt was the best singletap practice in this game, and when I was close to finishing my session I'd spam Worldwide Choppers until I couldn't tap anymore and ended up fingerlocking due to fatigue.
For 500 tortures, WWC and Kokou I'd also replay them again and forced myself to use K1, and then I did it again for K2, because my normal playstyle is some bastardized singletapping where I shift between the dominant finger throughout the map, kinda singletapping but still ending up with something like 720/670.
I also believed that I'd never be able to develop the proper fingercontrol for val0108 maps, so I just forced myself to singletap them all (and I played them a lot back then).
While that was absolutely disgusting for my acc, I feel this also contributed to improving my speed because I'd just try to still play the BPM properly, which lead me to the conclusion that the common advice of "Slowly going up the BPM" is absolute BS if you really want to get fast quickly.
Getting fast is just related to working your fingers really really hard, and if you never force your fingers out of your comfort zone and start feeling the burn and finger locks you'll either never be able to play high BPM, or just take ages to get there.
I started in late february and was able to singletap and burst 240-250BPM~ around 3 months later, and I wasted an entire month being an alternator prior to that.
I still can't stream high BPM properly, but contrary to what seems to be popular belief high BPM isn't some seperate "being". The reason I can't stream high BPM properly (long streams that is) is that I can't stream regular BPM properly either.
As long as you have the speed and the reading, all the other things easily transfer over to high BPM, so the only thing that you have to practice is speed. Same applies to aim. I almost never played high BPM aim maps, but practiced a lot of regular aim maps / pp maps, and when I played maps like Highscore etc I was still able to play them comfortably.
Aim, Fingercontrol, reading of certain patterns all transfer over to high BPM and aren't a thing you have to exclusively practice again on high BPM maps. You don't have to spam ILY and Highscore to get good at high BPM aim maps, and you don't have to practice high BPM finger control when you already have finger control.
There are some occassions where skills don't seem to transfer because the map is really dense because of the high BPM but a lower AR, which can delude you into thinking you lack other skills when it's actually just the reading that's not good enough.
Anyway, TL;DR
I'd honestly just spam high BPM maps, preferably Yousei Teikoku because the AR is usually lower and you get better reading on dense maps that way. As I said my big favourite is Kokou no Sousei for that matter and 500 Tortures and maybe on the level you're at you could try Worldwide Choppers, too.
Zetsubo Plantation is really good if you want higher spacing and not just the closely packed singletaps, but I think you should minimize most other skills needed to play so you can concentrate fully on improving one thing (speed in that case)
Kokou no Souseis singletaps are very close so the aim aspect is diminished and it doesn't require any finger control, which puts way less strain and stress on you as you play and you can focus on your left hand and the required speed.
If you don't have speed for certain maps I wouldn't quit, I'd just try to go as fast as you can, even if your acc suffers from it.
Imo if you don't expose your fingers to higher speeds and harder, physical demand your body won't make the required changes you need to be able to play them.
Just play Yousei Teikoku and all the other maps mentioned throughout the day and b4 you quit your session and do it consistently every day or second day so your body actually starts developing speed.
It's just like anything else. If you just lift light weights your entire life, you still won't be able to lift heavy weights.
I wouldn't try to practice combined skills specifically, but I wouldn't try to avoid them either. As I said, I didn't really play high BPM aim stuff, but I was able to do so eventually because I practiced high BPM early, and when I finally practiced aim, I was simply able to do higher BPM jump maps. It was the same for bursts and streams for me. (I learned bursts early bcz Koko is full of them, though.)
Same reason why most people can't singletap 280 BPM, but most can atleast do 240BPM. They just never try to do it or force themselves to do it, so their body never made the necessary changes since they never had to go over 240BPM.
If you can alternate high BPM fine, that's one option, too.
edit: wasnt really tl;dr lul
