C half diminished = C, Eb, Gb, Bb and already has a sharp two in it in the form of the b3 there. But as a convention we don't use "sharp" for the two in most instances of fake chording.

I haven't heard the target tune, but I'd almost bet that what you are really looking for would be the C7#9 chord.

Try it and see.

If not, the C half diminished by itself should work, you might add whatever note extra that really is in the Melody track as it may be a shared Melody note.

To get a D natural in there, you might try EbmMaj7/C which in closed position would yield, C(bass), Eb, Gb, Bb, and D



--Mac