(Author here)
The DERP server is already open source and tailcat can use any DERP server you run: https://github.com/tailscale/tailscale/tree/main/cmd/derper#...
We just provide some default ones (https://tailcat.dev/derpmap.json) to get started if you're not bandwidth-sensitive. But you don't have to use them.
Update: I added more explicit docs about this to https://github.com/tailscale/tailcat#bring-your-own-derp-rel...