Update: It turns out the customer service boss did try to call me back. Unfortunately, he called me back at the number I had called him from, and not the number I left for him in the message. As a result I didn't get the call, and it took a couple of hours before I received his voicemail. So that is not quite the lapse it initially seemed.
However. When I called him back, he did (very apologetically) confirm that the work is not finished today as promised, and the technicians went home without providing an update other than that it's a "difficult instrument." He stated that he believes I'm being more than reasonable, and he promised to make it his mission to get it moving on Monday. I agreed to talk on Monday. Afterwards, I texted him to add (politely) that I really want to know in what way it's difficult, and how that brought us to this point, and suggested maybe if they can't fix it they should replace it. I said I know they don't just have them lying around, but I'm sure they could build one in less time. So we'll see what he says to that on Monday.
Regarding the email link idea: I appreciate the willingness to help, but I feel like it would probably do more harm than good for them to get all those emails and have to reply to each one. It risks descending the situation into chaos, so I'm going to table that idea for now. But thanks.
Well, they were working today, as it turned out, so I would have to say either "yes" or "it isn't relevant here."