To increase height, bring your non kicking leg higher in the air and try your best to jump. At this point, since you have the technique, you just need to get stronger jumping and timing the kick.
Personally, when I was learning this kick, I was able to do it but similar to what you're experiencing, kicking very low. And every time I thought to jump higher, I wouldn't do the proper twist and end up just doing a normal 360 kick.
The "breakthrough" I experienced jumping higher was by adding a round kick/step
right before I attempted the move. For some reason it triggered my body to increase height yet get the same turn I wanted. (This has worked for a few of my students). Another way would be to trying to
stick a hook kick as soon as you land. Finally, what I strongly recommend is for you to aim starting at knee height than gradually increasing height (If you don't have access to a studio, a friend holding a slipper/piece of paper/pillow/hand/ does the trick for a target! lol) . Leaning back works for some too, although it may feel a little scary at first.
Hope this helps! And if you have more questions, or need clarification let me know
