Welcome to the forum, jersyknollfarm. I made Brie a couple of times, with 2 round Brie forms that are 23 cm diameter and about 9 cm high. No bottom.
While draining, I use for every mould a food grade PVC tray with holes in it, a cheese mat upon that, covered with a cheese cloth. On top of the cheese cloth the mould with the draining curd. When I have to flip, I have an extra set of tray, mat and cloth which I put on top of the mould. Then I grab the two trays together and flip it all. And yes, that's tricky but you can practice with rice instead of curd.