Submit the amended return. Challenge HMRC's decision if they reject it.
Unfortunately, if you're planning to make a gift based on the net costs to yourself you need to know what the effective tax rate would be.
e.g. you want to make a net 10K gift.
If the tax relief is 40% then you should give 13333 - the charity reclaims 3333 and you reclaim 3333 meaning you have 10K less in your bank account.
If the tax relief is 20% then you should give 10000 - the charity reclaims 2500 and you reclaim nothing.
Safest would probably be to give 10K and submit the amended return. If the claim is not rejected then gift the additional 2500 you reclaimed in another tax year. The charity will get 15333 instead of 16666 but you're at no risk of paying out more than you intended.
The moral of this story is to never submit your tax return until the last possible date...