There is a grace period - just that it is before the application date. They advice applications be done 28 days before to cater for these.
As to them being flexible in cases of such circumstances, it will be your luck. There seems to be no official policy on that. And I can understand that - if they make the grace period official, it will just be treated as additional time by some people.
You should do that anyway. But again, there is no guarantee. If something goes wrong, the bank is not going to help you get through UKVI.
The chances of a Debit card rejection is generally quite low if you have the amount in your bank account.
Overall the risk is low, so it is up to you whether you take it or do the surer option of a bankers draft