So I tested out the option of making the game free to download without a reward, and then disabling new downloads/purchases at some point. But I realized that this option won't work for what I'm trying to do, because people who got the game for free don't "own" the game. So if I disable new downloads/purchases at some point, people who have downloaded the game for free will no longer have access to it.
I think instead, I'm just going to make my Itch.io page Restricted, and generate bulk keys to distribute to people. This will work well for giving out keys at physical events, as I can just print them out and distribute them. However, I'm still trying to figure out a good way of distributing a limited number of keys to people online who want to sign up for the playtest. Does anyone happen to know of a good way of doing this, without running into the issue of sending multiple people the same key?