Jake,
I'm one of the sailors who angles the cleat up so I cannot cleat it from the wire. The main reason I do it is so when I am wild thinging downwind, it does not cleat as I play the mainsheet.
For tacking, like Ken Marshack, I transfer the sheet to my tiller hand and grip hard. I use the freed up forward hand to grab the trapeze handle to come off the wire as I push the tiller over. The main eases some but not enough to stop the tack. As the mainsail tacks, I ease the sheet a bit more and cleat it, and then make the swap to the new tack. I agree with Ken that you have to go out and do a lot of practice. I also agree with Ken that once you get the system down, it is faster than cleating and recleating.