I have a new toy!
It’s a batt-holder. Basically, a circle of MDF-type stuff with a square cut out in the middle, which you can fit a standard commercial 6-inch tile into. You attach your holder to your wheelhead, you put your tile in the hole, and you throw whatever you want on top of it.
When you’re done you just pry your tile out of the hole and put it wherever you let things dry. No cutting and sliding freshly-thrown things off the wheel means less chance of warping or collapsing in transit. And it’s waaaay easier than attaching and detaching batts one at a time for each pot you throw, which is what I was doing previously.