ARD stock at "determining target computer status"

I've got a lab of 2013 iMacs setup at school, currently with Catalina running successfully. I'm managing them from a MacBook Pro with Monterey via Remote Desktop.

This works great on 29 of the identical machines. On the last one, I can connect and screen-share the machine, but whenever I try to run a command (or remote restart, etc) it stalls at this prompt:

"determining target computer status"

I've re-installed from scratch on this machine twice now, and everything else appears to work fine. The settings are theoretically identical to the machines next to it...

Is there any reason a hardware issue would cause this particular problem, when I can still successfully screen-share on it (so I know the network connection is good)...?

Where should I begin to troubleshoot?

(and on these machines upgrading past Catalina isn't really an option, I believe...)

Thanks!

David