I'm in a similar position and, having not paid the balance beyond deposit, I'm just going to request the deposit voucher using the online system and rebook something entirely new.
Saves you the hours of phone calls.
Last time I had to make changes due to flight cancellation the agent totally borked the booking anyway, resulting in an impossible itinerary - so had to call again (cue more hours).
Save yourself the time.
Also, if you're not booking for a Double Tier Point promotion then avoid BAH for the very reason it's a separate entity and contact is incredibly difficult. I'm BA direct and Expedia 'pay when you stay' now.