I've made the first pass with the milling machine on the glass rest. It now has a slot to pass the stem of an up glass or other stemware.
I still need to chamfer the edges, but I'm taking it home first to double check whether I might need to make the slot a bit wider first (for reference, the whole thing has an outer diameter of 4"). Then I have to mill a well for the glass-detecting microswitch, and the counterbored hole to bolt it onto the support arm.
I should get everything done on time. I also made a quick pair of small outrigger panels to hold two more pumps.