EDIT:
Posted while typing.
HICKS
If HICKS - 1, H???? is proved. 2nd letter cannot be I through NIFTY - 1; ??CKS are all impossible by NICKS - 0.
If HICKS - 0, ?A??? is proved.
HASTE - 2: where H is disproved by HICKS - 0; ??CKS is disproved by NICKS - 0.
PUNTS
IF PUNTS = 1, ???T? is proven, as PUNKS = 0; score change while the only letter change is T-->K
IF PUNTS = 0, I will come back and later prove the F or Y from NIFTY.