how do I change the capitalization of my gamertag without paying twice

There is no other way. The system doesn't see things like capitalization as making a gamertag unique. So you'd have to change it to free it up to something else and then change it back (and hope nobody else also has it so you don't get a suffix).

The only way to change it would be to change the gamertag to something else and then change it back with the correct capitalization. You would have to pay twice.

It will actually cost you 1600 Points because you'll have to change it twice.

Since gamertags can't differ only by capitalization or spacing, you won't be able to change directly to a version with only a capital letter change. You'll have to pay 800 Points to change it to something truly different, then another 800 to change it back
to the original gamertag with different capitalization.

Oh, I understand. But can I change the capitalization of the gamertag using the paid name-change?

Yes, following the instructions bowski gave you, so you would have to pay twice.

Hi there The Figure! As has been said, this is something that we aren't able to change for you. Ideally the system will pick up the proper capitalization but otherwise you'll have to pay to change your gamertag twice if you'd like that 'F' capitalized, once
to free up your current gamertag and then a second time to change it back. Sorry for any inconvenience here!