Yes, you can pay the $10 for the EBCI on a companion fare ticket. I have done it many times in the past for my husband.
Just FYI- the ONLY time I have ever seen a gate agent allow a companion to board with the main passenger, whether BS or A-List preferred or whatever, is when that companion was a child, and I have only seen it once. Rules quite clearly state that the companion boards separately with their own boarding pass. Of course, if you are wary of leaving your 11 year old in the waiting area while you board, you can always board with your companion at the later position-
Can groups assigned to different boarding positions board together?
Yes. However, in order to maintain the integrity of the boarding process, we ask that earlier boarding positions board with the later positions. For example, if a passenger is assigned position A16 and wants to board with a passenger assigned position A45, the passenger holding the A16 boarding pass should board with the A45 passenger.