A separate thought - have you looked at the cost of booking the same holiday now separately, either with the same flights or on other airlines (EK, VS) and both as a package or as individual elements?

It may be possible that you can find the same thing for similar price to the remaining balance you had to pay, or at least within the 5k more that you were willing to pay. Don't assume that the price BAH is offering is the best one out there.

In other words, even if you can't get anywhere with BA crediting the lost deposit (which seems harsh but I get is as per the rules), you might be able to mitigate it by rebooking in a different way anyway.