In modeling, orient the view to the desired position, choose View -> operation -> save as... and give the view a unique name that makes sense to you. Switch to drafting, insert a base view and choose the view you just created.
Try customizing your menu to add the "save as" option, or switch to a role with full menus (warning: changing your role may replace customizations to your toolbars/layout; save your current layout as a new role before experimenting).
You can make a section in air that points torwards the hole that you need dimensioned at the correct angle. This also will allow you dimension your view angle also.
Then in your view label change your view label from Section to View.
Well I was able to get the view I needed by simply just adding the projected view and the new view snaps in place as you move it around the previous view.
If you can see the hole in a another drawing view, you can (as it sounds like you've found) project a view using the hole as the defining vector. See the attached movie for a simple example to which I'm referring.