well, it's been a long time but I'm still working on this.
I spent the last weeks fighting with an Arduino, some photo-transistors, an LCD display, and I now have a somewhat functional shutter tester. I may share the design if you're interested (that will be when I'm finished with it so I hope you're not in a hurry).
Today I could check the speeds again and finally the speeds up to 1/60 are OK, then the higher ones tend to be too fast, until 1/1000 and 1/2000 which do no trigger the left part of the sensor. This confirms the shutter capping.
I measured the travel times for the two curtains, and what I get is that the first curtain crosses in 11ms, and the second takes 10, so this is consistent with what I'm seeing. I have to check the program as I guess that these integer values likely mean I'm rounding or truncating and the difference might be slightly different (no pun intended). At the moment, modeling this is a spreadsheet confirms the difference in travel time might not be exactly 1ms.
(the difference here is what I measure vs what I compute, not the speeds accuracy)
I also noticed that the "rolling shutter" effect happens also on my laptop's display, so this could be a quick and dirty check of a shutter's speeds.
The plan for the coming days is to improve my slow and dirty build of a shutter tester, check the exact travel times, and devise a way to make them equal. My guess is that I should find a way to "untighten" the second curtain, so that it does not try to overpass its brother.
If you have thoughts about this, I'll be happy to hear from you!