So now that I have the mount, I'll answer my own questions, for the benefit of the next person. Yes, the hand controller's WiFi setup is happy to accommodate other devices. In particular, StellarMate advertises itself as "stellarmate.local" on this network just as it does when using the WiFi hotspot put up by the Pi itself. So that means that I can set up the Pi to join the hand controller's network, and also connect to it with a laptop. Ekos talks to the mount just fine, and I can VNC in to the Pi.

The only downside is that the hand controller's WiFi signal is pretty weak; the Pi couldn't see it from across the house. So that might obviate being able to sit inside with the laptop and control everything from there.

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