Thanks for posting those, and for the reminder of how bonkers and creative the Leslie-hosted version of TPIR was.
Partners is like a lot of the new games in this version - a few great concepts in there but it doesn't entirely hit the mark. Having the main contestant choose between two prizes and the second contestant selecting the correct price from three options is great, and giving the first contestant a 'right of reply' as to whether they agree with that price is particularly interesting.
However, it seems a little bit flawed to ask the first contestant whether they'd rather choose "the higher price" or "the lower price" instead of the chosen price, when the second contestant could well have chosen the highest or lowest of the three options. A better option would've been for Leslie to say upfront that the second contestant will select one of three prices, and that you must decide whether the actual price is higher, lower or on the nose. Or alternatively - ask the second contestant to select two of the three prices that they think are most likely the price, then have the first contestant select one of those two as the price of the item. That way they both still have a say in the final outcome.
And yes as you say, Tic Tac Toe applies the On The Nose-style pricing portion to the Secret X/Joker main game where the contestant can earn all but one of the available options to win the main prize. I actually really like the concept of combining those ideas, although I really dislike the staging of the game.