Isn't this a good reason to push, so you can thin the field and not be up against 5 hands?
I hate the idea of pushing into the nuts too, but I also hate both the ideas of folding a set here and calling. I wouldn't want to throw in 220 chips and then face a semi-bluff raise from someone else, or just have a few people call and not know what the heck to do on the turn (or worse, to see a 4th diamond fall).
I don't know, I hate these hands where it seems like you have to choose the least worst option.
Its too late to thin a flopped flush from the field, and you dont want to thin the field if there is no flopped flush, you are a favorite and want as much action as you can get. You love a semi-bluff behind you but I doubt youll get one. Why are you afraid of the semibluff if you were going to push anyway?
The only hand that pushing helps against is an overset and the push folds it out fearing a flush, but set over set is so rare I dont think it changes the decision. Think of it this way...with a set you are WA/WB here, and that calls for playing but keeping your chip commitment small. If a couple of the players behind you call thats even better, its more likely that diamonds are duplicated.