It's not a bad play with read. 

I would 4bet to $6 because I need these range to balance my 4bet/bluffs so it hurts me if I don't use it. The aim is to have my opponent see FE in the 5bet/shoves. 

As played, calling down is OK but I might actually raise turn because I think it improves his SB flatting range somewhat and missing value there by being too rigid to remain passive probably is not a good idea. We should keep our options open and react optimally to different board textures and the opponent archetypes. 

Hi, For what its worth i like the play....i think it unlikely that he'll barrel  all 3 street with air, so i think by raising turn you make the river alot easier, also any hand that's going to bet almost pot  on the river that isnt a bluff is most likely calling a turn raise...

So by raising turn you get a bit of info, and get to build a pot with the best hand (most of the time), plus i have a feeling that he was probably betting big if say a blank 2 hit river...

if you raise turn and vill flats you're looking at between 35 and 40 in the pot...and both you nd the vill will only have a small amount behind, so when a blank hits the river you get the extra part of his stack almost always...if he checks and you bet, i cant see a vill like this folding for such a small price...