I would change the Choice Specs set to this:
name: Choice Specs
move 1: Leaf Storm
move 2: Psychic
move 3: Hidden Power Ground / Sleep Powder
move 4: Giga Drain
item: Choice Specs
evs: 132 HP / 252 SpA / 124 Spe
Giga Drain /needs/ to be the main slash. Recovery + attacking is so useful for a Pokemon like Exeggutor, because it will be taking many heavy blows. Giga Drain greatly assists in alleviating those heavy blows. I actually find myself using Giga Drain much more often than Leaf Storm.
Skuntank's prominence in the NU metagame makes Hidden Power Ground very important. It's arguably the best answer to Exeggutor, and if you can snipe it on the switch, you just took care of a potentially huge threat to the team. Altaria is not particularly common to warrant using Hidden Power Ice and being locked to Hidden Power in general sucks.
Hidden Power Ice would go in AC if you change the set to this.
Also, Psyshock is not as awful as you make it out to beat. Besides Lickilicky, it also hits Altaria, Flareon, and Regice harder. The latter two are increasingly more common with the new hail meta.
The rest of this skeleton looks fine so far.