Here is where I'm at on this problem, pretty close I would say, short of looking around for a professional negative scanner.
Flatbed scanner, lid open
@Rafal first suggested I have a look at Alexey Alexeev's "Scanning Wet-Plate Collodion Ambrotype or Tintype Plate" on YouTube. It certainly looked promising. Alexey's photos are great by the way, check his work. He recommends leaving the scanner lid open in his video. I gave it a shot but didn't achieve anything usable (see below), most likely because his plates are collodion ambrotypes/tintypes, not negatives. I contacted him and he confirmed that statement.
Flatbed scanner, lid closed
Next I tried closing the lid and scanned the negative plate that way, following the previously mentioned video to adjust the input and output levels. Here is what I obtained (below), without any cleaning involved. I was not convinced that's what I should expect though. Alexey confirmed this was not quite right, most likely because light was bouncing off the cover and the glass plate.
Camera on a tripod, shooting down at a lightbox
Finally my father and I built some kind of lightbox out of a small wine box, a light bulb, some cardboard, and Plexiglas. It's really just a fancy shoe box with one side replaced with a sheet of Plexi :) I used some tracing paper to provide diffusion and placed the negative plate on the box, the light shining from below. I'll post a picture of the contraption later. I setup my tripod on top of the box and my Canon 5D Mark II shooting down at the plate. I turned off all the lights and took a few pics at different parameters. I got the best result at f/8, 1/10th s. and ISO200. I used a 2 seconds timer and mirror lock-up to reduce vibrations. I opened the photo in Lightroom, inverted it using a preset, fixed the white-balance, adjusted the levels and removed a few dust spots.
I think that's as good as it will get for this little vacation project. The box is easy enough to build, especially if your father is retired.