score:8
It seems to me that there are no painless, cost-free options for you. (Note that a D visa application will take significant effort from you even if the university would help. It is more than just some paperwork.)
I'm not in your position, but I'd probably go for leaving in between (two whole days). Ever been to the UK? That should be possible for less than €500 if you plan well ahead. A bus ticket should be less than €100, and there are many nice, scenic towns with cheaper stays than London. Just make sure that you cross the border before midnight on Friday and after midnight on Monday.