display/greeter-setup-script in one seat is blocking greeter session in the other ones

In my multi-seat setup, I want to run a pre-greeter script (configured via display/greeter-setup-script) that waits for user input before greeter starts in some seats. However, I'm observing that my script is blocking lightdm in such a way that the next seat's greeter will only be spawned when the previous seat's display/greeter-setup-script has finished.

Is there a way to make lightdm spawn my display/greeter-setup-scripts in a non-blocking way?

P.S.: I've already thought about the possibility to use a greeter-wrapper rather than a greeter-setup-script, but greeter-wrapper is run as lightdm user, right? In this case, my wrapper script would fail, unless user lightdm is member of group input.

Start by tracing how display/greeter-setup-script is launched and how lightdm handles the next seat, then compare that path with greeter-wrapper and its lightdm-user permissions. Done means setup scripts in one seat no longer prevent other seats from spawning their greeters, with the intended behavior covered by tests.