CLOSED
If 3 then D is last as the only change from CLOSET to CLOSED wad T->D and the score raised one.
If the above is not true, try:
CLOSES
if 3 then S is last as the only change from CLOSET->CLOSES was T->S and the score raised one.
If that is indeed true, disregard the rest of my post.
However, if CLOSES is still 2, try:
CLOVES
S is already disproven, as the score didn't change from CLOSET even though the S was a different letter. So the only (other) change was S->V and if 3, then V is third as the only change from CLOSES to CLOVES was S->V and the score raised.
If 1 then S is third as the only change from CLOSES to CLOVES was S->V and the score dropped one.
If the above is true, disregard anything else I say.
If still 2, try
GLOVES
If 3 then G is first as the only change from CLOVES to GLOVES was C->G but the score added one.
If 1 then C is first as the only change from CLOVES to GLOVES was C->G but the score dropped one,
If still two, try;
GROVES
If 3, then R is second as the only change from GLOVES to GROVES was L->R and the score added one.
If 1, then L is second as the only change from GLOVES to GROVES was L->R and the score dropped one.
If GROVES is still two, then O is third and E is fifth as all other letters that could score are disproven, and these are the only two letters left to score.