Cost reducers normally apply to turns, for instance Ferry:
Move your -$2 cost token to an Action Supply pile. (Cards from that pile cost $2 less on your turns, but not less than $0.)
So at the end of the game, when you're tallying points, it's not "your turn" (or anybody's turn) so the cards just have their normal costs.
Family of Inventors says:
This makes cards cost less at all times for all players, not just for the player placing the token.
"At all times" I guess also refers to the end of the game so I would think cards still cost less at that point.
With regards to Duration cost reducers: at the end of the game you just put all of your cards in one big pile and start counting so even Duration cards, although they might not have been discarded during the clean-up phase, still end up in that pile and are not doing anything anymore.