Not sure if I should call HR directly and ask, as I said the pool letter doesn't sound like they're sitting by the phone waiting for folks to call and ask when they can start.
I would talk to the HR but in person and not on the phone; I’d try to meet up with them at one of the job fairs, any job fair. Several folks in the HR have been promoted to different positions since you interviewed, also there’ve been many changes in the online application. I think showing up in person would only indicate how very serious you’re about joining Big Brown. That’s just what I’d have done; maybe having your sponsor call the HR would work too? I think that’s better than you calling them - after all they did instruct you not to call them - 5 months or not. However, you never got any instructions on not seeing them at a job fair again, did you?
Good luck to you!