OP has a CC statement showing that his account was debited for the room and a statement from the property showing the stay and a $0 balance. Not sure what else anyone could want or supply. Perhaps less messy on one piece of paper, but I do not see Wyndham or any other chain or individual property altering its accounting practices because OP's employer can't take two pieces of paper rather than one.

This sounds more like a labor dispute than a hotel issue.