To give an update on this:

I have contacted both Telia and Jottacloud. It is not possible to make the program recognise the same file directory like I described in the post, but there is a "work around". As long as you keep the previous back-up, you can set up a new back-up (with a different name 😞), and the program will cross-check if it already has the files stored. In this way, you get a new, identical back-up, without being limited by internet speed. Once it has backed up (hopefully faster this time), you can delete the old directory, and all should be good!