My .02 -
Late May brings the smaller fish, eager to eat anything you throw once you find their stationing behavior thru tide changes. Early June the numbers increase, and by mid-June things are well out of control all over the area with big and small fish mixed in. By late June the area is settling into it's resident / transient patterns and by July the fish that are going to hang out through the summer - "residents" (which I believe are packs of roving fish covering the whole Monomoy area in ever-increasing regularity of patterns thru the summer). This is when things get challenging, and the angler is put to the test for wit and will.
By late August the area surges back into form, and with the exception of last year September brings another explosive wave of eager fish - including tunoids to the Monomoy backwaters.
Last year's abundance of sand eels on the outside and big bass along with them - might have affected the fall Monomoy wave somehow, who knows.
Anyway, my opinion on the question: if you want solid action with large fish in the mix, I'd target early to mid-June. Try all the access points, SB (inside / outside), NM (crib, channel, north end, west flats, etc). Look for patterns of moving fish and when they station. If the juvie squid are around there will be big bass around in shallow water.
But if you want the quintessential high sun sight fishing cat and mouse experience, wait until late June / July. You will have a much higher fish/frustration ratio but will come out a warrior of the flats game. The earlier season is great fishing but teaches you very little in this respect.
How about BOTH!