‘But as we are experiencing something - a perception, a thought, an emotion, a memory, etc. - whatever it is that we are directly experiencing in the present must, by definition, exist in the present as it is being experienced.’

This is a fallacy of equivocation.

‘Whatever it is that we are directly experiencing in the present’ might mean

(1) Whatever it is we have a present experience of

or

(2) Whatever it is in the present that we are experiencing.

Your assertion is true for (2) but it simply doesn’t follow that it is true for (1),
which is what your argument needs. Indeed, put in (1) and your assertion is false,
for it isn’t true BY DEFINITION that whatever it is that we have a present experience of must exist in the present.