This solution does almost what I want it to.
Only thing is, I have my menu set up as follows:
Menu item 1 Menu item 2 Custom post type 1 Custom post type 2 Custom post type 3 Menu item 3
Using the solution I mention adds the tag "current_url" to the sub menu of the custom post type I'm in ("Custom post type 1"). But I want it to add a "current_menu_item" (or something) to "Menu item 2".
Any way to do this?