I don't know if this has been implemented or if it's a fluke or what, but I am now able to sync borrowed books from multiple library accounts while only signed into one library on my kobo.
So here is how I have it set up: I have one overdrive account that I log into online with my email and password. All my libraries are attached to the same overdrive account. When I log into my overdrive on my kobo, I pick one of my libraries but log in via my overdrive account (not my library card #).
When I borrow books online from any of my libraries, they all transfer over when I sync my kobo (I don't have to log in and out of multiple libraries on my kobo). Have they changed something to make this happen or is this a fluke? Either way I'm rather enjoying it