Im just going to throw out there that I've been playing Stall Exeggcute for a few weeks now for LC challenge, and it does not suck. You say sleep interferes with tspikes? You are flat out wrong. You say Exeggcute is set up bait? You are once again, flat out wrong. You say Harvest is too unreliable or it is too weak to stall effectively? You are once again wrong.
Now that that's out of the way, let's go for
Balanced / Sandstorm
As I said, I've used stall, but that is a completely different manner of playing eggy. I do not think we should do hyper offense, and here's why: when it comes to Hyper Offense, Gastly does Exeggcute's job better. Gastly can also use sleep moves and has better STABs. Exeggcute's niche is being able to stick around longer.
Croagunk is an awesome teammate, being a solid check to Scraggy, and absorbing TSpikes. Priority is also nice.
The reason I've slashed Sandstorm in is because Exeggcute handles one of the main things Sandstorm struggles with: Bulky Water-types. Exeggcute complements Drilbur in numerous ways: notably, he can lure in something like Bronzor or Ferroseed and put it to sleep, giving Drilbur extra opportunities to set up Swords Dance. Hippopotas nearly always gets Stealth Rock set up, which also benefits Exeggcute.
In reply to the above post, Houndour is a nice partner, I've tested it.
AND FINALLY, can we please not do stall with Exeggcute and Tentacool core- I still need my team for the lc challenge to not be completely stale :D