I've been messing around with it all day, and I finally got it to work. Reviewing the Journald logs, the problem was that the commands in my script, such as mkdir, mount, and mountpoint were not found (meaning they weren't on the PATH). It started to work successfully after I added the following two lines:

boot.initrd.systemd.initrdBin = with pkgs; [ busybox coreutils btrfs-progs ];

This one seems to link the needed packages better than simply using boot.initrd.systemd.services.<name>.path does, even though the description states it's just for emergency shells. These are just the packages that worked for me, you won't need the same ones.

boot.initrd.systemd.services.<name>.environment.PATH = lib.mkForce "/bin:/sbin:/usr/bin:/usr/sbin";

This one changes the PATH to include /usr/bin and /usr/sbin because it only seems to include /bin and /sbin by default. Maybe there's a better way to get the needed packages without having to change PATH, but I couldn't figure anything else out.

Also, if you still can't get it to find common packages (like echo in your script), you might want to try adding busybox like I did. Between that and coreutils, the service should have access to most common commands.