I really don't know, I mean, look at all the action that happened, and than consider your options.
You stated "You're drawing to the nuts", yet you really weren't "Drawing to the nuts". The Nut's In this case would've been like "AQd/AKd", that's the nuts. You were drawing to the "Straight flush+OESD", those were really your only outs and nothing else.
Now as for the hand, I mean, action was, Raise+Flat+RR, and on to you, but while It's an ugly situation to really be In, I can't see how you can either, call In this spot, and I really can't see how you can shove In this spot TBH. Yeah, It's a "Straight Flush Draw+OESD", but even If you add up all the outs that you can possibly have at this time.
So what do you have 13(Diamonds)+3(7s)+3(Q)=19 Outs, and you have 2 of them In your hand, giving you 17 outs total. Now you can't count all the outs as being clean with the way the action Is going. I mean, really their just Is no way, after a raise+Call+Reraise, that you believe a "9 high flush draw" can be good, correct? Which than brings us to thinking about the 6 outs we do have, the 3(7)+3(Q). Now If we take discount AK, from the scenario (As their was no 3bet Pre), we don't have to worry once the "Queen" Hits, this Is of-course, assuming that 3 "Queens" are actually In play, In a table of 8-9 players, same thing with the "Sevens" they all need to be left In the deck and not In someone's hand. Than we only have (6) outs+The 2 extra straight flush outs that give us the nuts for a total of (8) outs. So going by just a mathematical observational stand point, It's really not worth going for.
While I do agree this Is a beautiful hand, you need to consider the fact that someone else could easily have a set+2 pair+ a higher flush draw, and thus easily Is dominating you.