Have you tried using the floating keyboard? I exclusively use it on my iPad not only for saving the screen real estate but also because I can swype on it (even though I can touch type on the big on-screen keyboard just fine; I still find it more convenient to swype with one of my thumbs, or the pencil https://support.apple.com/en-us/111789
Thanks! I haven't -- or, at least, not in a long time. Wow, the UX is terrible! I accidentally first dragged my kyeboard into split mode before reading the instructions. Then I've managed to get it into floating but it was hard to re-dock, and the first few times i tried to move it anywhere, i got some unintended feature enabled. Yikes.
I'll have to remember to use it next time i'm bothered by it covering some control. I still haven't made friends with swype, but I do use it occasionally.
Yes, I remember it being really finnicky when it was first released, and lots of head scratching getting the docked version back. I don't know which iOS version you're using, but I was pleasantly surprised by the newer ability to pinch/reversepinch to shrink/grow it between floating and docked in newer versions, I think that's a recent development.