I'd really like to know if there's an easy way to get my pilot profiles back, though I guess it's not the end of the world if I have to start over on some things. At least I'm between campaigns on the stream, so that's not a huge issue. I had lots of shiny medals in FreeSpace and FreeSpace 2 though. 
I did confirm that forcing FreeSpace Port to run on 21.5.x solves the issue, though I'm also hesitant to run on a development build for streaming (and in general) and risk... "surprises". Is there no way to convert my profile back to 21.4?
The pilot file was converted to use the new controls5 code when you started the 21.5.x build. At the moment, there is no way to convert pilot profiles back to 21.4-compatible. Until the new controls code is stabilized, the recommended procedure is:
1) Back up your pilot files somewhere
2) Delete the most recently used pilot files from the pilots folder
3) Run a pre-controls5 build, such as 21.4 stable
4) Create a new pilot, or use a pilot that was not selected or used when you ran the 21.5.x build
Once the controls5 code is stabilized and 22.0 stable is released, you'll be able to use your backed up pilot again. Even so, it still may not be possible to backwards-convert pilot files; that remains to be seen.