Not very helpful for the OP, but I do partly what DeathSlam suggests. I pay the minimum deposit plus I round it up to an even number. e.g. if the holiday is £3294 and I am asked for a £200 deposit I will pay £294, to leave £3000 to pay. My thinking is that (in the unlikely event) I forget then at least BA can see I have not just paid the minimum and I do intend to take the holiday.
Then about a month before it is due I might pay another £500, with the last bit at least 4-5 days before it is due.

However I think that the real solution would be for BA to:
a) email, text and possibly call (could be an automated message) customers to remind them a few days in advance
b) offer alternative payment facilities such as a Direct Debit or Continuous Payment Authority on a credit card, so the due date is not missed.

I am very bemused that BA does not seem to have a process/system in place to ensure they are not losing a £25k booking. Bizarre.
Finally, I am not a lawyer, but I think the OP may have a case against BA under the terms of Unfair Contracts. I think a good lawyer could argue that BA were being unreasonable, given the amounts involved, by not a) attempting to contact the customer and b) not accepting medical evidence of ‘force majeure’ as the reason the payment was delayed.