"And on the other hand, I sometimes do have two projects for the SAME customer open at once (such as two versions of the same studio design, with different layouts, that he's going to choose from later) and I'd like the work done on both of those to accumulate on one single clock"
SK man 2020:
Yes you can choose to create a different SU clock counter for each project, and even if you have multiple projects windows opened (if you have enough RAM), the clock will adjust to the front window project timer. That's the greatness of this tool (thank you Fredo!) On the other hand if you have two projects for the same client, you can choose to add the timer of your second project to the first one already created. It does appear on the dialog when you create a new clock. You have the choice to create a completely new clock or affect the timer to an existing clock. Usually you have the list of the most recently active clocks/projects and you can choose with one click to add your new timer to an existing one.
Hope this is clear enough (?) Cheers