Hmm, interesting spot.  Here are my thoughts.

The flat pre seems fine, readless getting it in here is optimistic at best.  3 betting isnt the worst of the options, but its effectively turning a great hand into a meh spot.

On the flop we have a couple things going on.  We have the best hand here a majority of the time.  Is shoving profitable? yes obviously we have a set lol.  However lets look at calling here. First lets evaluate the cards that we dont want to see.  Bascially if we call, we expect the two bad limpers(MP2 may not be bad but whatever) to call with anything resembling a draw.  The cards we dont want to see are a/k/8/9, all other cards are somehwat fine for us.

Now before you say it, i know there is a flush draw, the problem arises with whether or not a shove is getting these flush draws to fold.  what we are most worried about here with flatting is keeping in hands that would fold to a shove(something like A9 or something), and letting them get there.  Odds are anybody that got to this flop with two spades is now never folding.

So we are afraid of 4 cards, or about 25% of the deck(roughly).  So 75% of the time on the turn we expect to be happy about where we stand and can get it in, again with the best hand a lot. 

Obviously are goal when flatting here is to get money in from the 2 people that checked that wouldnt have put money in if we shoved.  So if you have a read they will do this a lot, then I like calling.

Shoving on the other hand, is definitely +EV and takes out a lot of the guesswork.  I would probably default to shoving here without reads that the two limpers are going to donate/spaz.

Shoving also has the added value of getting max value when flush draws miss, its not guaranteed a flush draw will gii with you on the turn if its a blank. with only 1 card to come.  however calling could get a weak hand to check shove frmoa  limper, then CO can get in a ahnd liek AA/KK/AQ thnking he has to have a better hand then you lol.  This spot can really go either way.