I found a piece of scrap wood that neatly fits between into the narrow vertical side space. Installed it with a hinge and added an RPi:

The RPi will be in my local WiFi and grant me access to the scope's LAN connection. It will probably be "closed" during normal usage, but I can open the RPi flap and add stuff for testing if I desire to do so.

The scope mount is probably too simple, but it does the job quite well. Two pieces of a cable channel with a cutout, screwed to the front, for the scope to "slide" in, and a piece of pipe to keep it from sliding to the back:

Here's a picture with the scope, from behind: