I was surprised here when John suggested just getting it in on the flop so I fired up the equity calc to have a look.
Preflop the villain can be pretty wide here flatting in position, i'd say all pairs from JJ downwards, Im fairly sure QQ+ 3 bets. Any stats even a small number helps of course to range but i will assume competency.
Id also include all suited connectors down to 54 and all suited aces. So obviously preflop we are well ahead. On this flop there are a lot of hands that can raise, all sets obviously, but pretty much all suited diamond hands and all pairs 77 to JJ.I have shown those hands below and stuck it into the equity calc and this is what we get, 63% So a shove is ok if you think the villain will stack off with all these hands. The 6 combos of each of 77-JJ (30) outweighs the suited diamond combos (18).
Once you add in 7d then your equity drops to 43%, its a bad card for us against his raising range so as played we need to consider giving up on the turn, we still do have 2.77-1 on the turn and enough equity to justify the call, so if we call the turn the T is pretty much a brick but knocks us down to 40%. so a river call is still ok
we have to call 1.80 to win 5.57 getting 3-1 pot odds
the river call is correct with 40% equity. calling down isn't really bad but after the 7 comes on the turn we are losing more often than not and calling down is just marginally better than breakeven.
So my conclusion is that John's suggestion of reraising the flop was the best time in terms of equity to get our money in. high variance but highest ev.
You can add in a few or take off a few combos but it doesn't change the overall findings.