How can I make a LaunchDaemon run an app at login?
@Wowfunhappy's suggestion to use a Login Hook got me the exact behavior I wanted, even if it wasn't done via a LaunchDaemon as planned. The solution:
A script (myscript.sh) to launch my app (must be executable via chmod a+x)
#!/bin/bash

//launch app in background (otherwise login hangs)
/path/to/myapp.app/Contents/MacOS/myapp &amp;

And specifying that script as a login hook via the command:
sudo defaults write com.apple.loginwindow LoginHook /path/to/myscript.sh

My app now runs as root as needed on every user login