GTO Brainteaser #9 -- Multistreet Theory: Range Building with Draws

This week we are going to examine a multi-street game, starting from the turn where one players range consists of the nuts and draws while his opponents range consists of a medium strength hand that never improves to the nuts.   I'll be going over this game in depth and providing a solution in part of my next CardRunners video which should come out in a few weeks.

Not that this is almost identical to the game that we examined in GTO Brainteaser #6 except that in this case, the hero's turn bluffs have the potential to improve on the river.  In both games the player with the merged range has about 50% equity (in this game he has 53.8%).

The setup is as follows:

1. There is a $100 pot, and we are on the turn with $150 effective stacks.  
2. The board is AsTs9c2d
3. The hero is in position and his range is 1/3 nuts, 1/3 straight draws and 1/3rd flush draws, specifically, the hero holds either 7s3s, 8h7h, AcAd.
4. The villains always holds a medium strength hand, KcKd
5. Both players are allowed to either check, bet 50% pot, or shove on both the turn and the river.
6. Your opponent plays GTO

The villain offers to always check the turn to you if you pay him $3 should you accept his offer?  What does GTO play look like in this game for both players?  Is this game higher EV or lower EV for the villain than the nuts/air game from GTO Brainteaser #6?

Would the hero be better or worse off if his range was 1/3 nuts 2/3 flush draws?  How would optimal play change?