+1 I like this suggestion.
As for an implementation of setting this priority: dragging the tags around could suffice. Although the favorited tag list appears on almost any page, maybe this functionality should be added only to the /prefs tab on the user profile page, so all other pages do not need load the script.
The more tricky part is how to take that priority into account? Any solution will break the default sorting order, won't it? But since the interesting page is personalized anyway, maybe that is not a great problem.
I noticed that the interesting tab is just one page, contains 90 items and goes (as of now) about 5 hours back in time. (What is the average time frame?) The driving algorithm already filters questions based on your favorite list, questions you previously watched and the ones you previously answerered (source).
I think the new algorithm should not reorder just that same 90 items, but instead it must pick a whole different set of items in order to take the priority into account. I think it will be a combination of the new priority index, the age, and the currently running algorithm.