An interesting deck. A few main problems I can think of is when you run out of 4 Eevee attackers, what will you do. Also, I'm wondering if you would want 3 Eeveelutions for attack and 1 for support (such as Glaceon), or a balanced 2:2.
So, the Pokemon.
Having a look at the Eeveelutions, I've noticed you are missing Flareon and Umbreon. Flareon is definitely helpful against VirGen and the new Metal Boxes, and certainly should be considered adding to the deck. Attack+Deoxys+Band+2 in Discard = 20+20+20+20 = 120 = 240 weakness.
Umbreon adds +20HP to all of your plasmas. So lets look out the positives and negatives of each of the Eeveelutions:
Espeon:
+s: Can snipe the bench and refresh hand.
-s: Low damage output --> Can't 2 hit KO any benched Psychic Weakness like Lucario and Mewtwo-EX. Any easy shot for defending Mewtwo-EX. IMO, Deoxys would be better as it can 1-hit KO a two energy Lucario and Mewtwo.
Best Matchups: Psychic Assault decks, Donphan (sniping), Garbodor (sniping) Lucario/Machamp,
Jolteon:
+s: Can stall EXs, 2-Hit KO Pokemon using Electric Defuse + 20 damage boost.
-s: Lower damage output - can only 1KO EXs with +30 Deoxys and +20 Band. First attack unreliable.
Best Matchups: Yveltal, stalling Seismitoad
Vaporeon:
+s: Can heal each Pokemon, has a high damage output against Fire-EX
-s: Low damage output against non-exs.
Best Matchups: Landorus, Donphan (maybe), Charizard, Pyroar
Leafeon:
+s: Versatile, can have high damage output for one energy
-s: Often situational but still practical
Best Matchups: Walls, Deluge
Flareon:
+s: Can provide a high damage output in many circumstances.
-s: Requires a decent set up as well as energy, low damage without setup
Best Matchups: Vir/Gen, Metal Boxes
Glaceon:
+s: -2 Retreat Cost for Plasmas, high damage output + sleep
-s: High energy Cost
Best Matchups: Landorus, Donphan (maybe), Charizard, Pyroar
Umbreon:
+s: +20 HP for plasmas, high damage output
-s: High energy cost
Best Matchups: Gengar
Main Problems:
No advantage over Aromatisse, Manetric-EX,
8 Eeveelutions is a workable amount, although some counts become unbalanced.
Firstly, decide what meta is around. If you rarely see Vir/Gen and Metal, is it worth putting in many, if at all, Flareon?
Secondly, do you want to focus on 'tools' as such. Do you want, or think is necessary, to have Umbreon's +20HP or Glaceon's Retreat Cost?
Thirdly, do any Eeveelutions clash? Glaceon and Vaporeon basically have the same matchups, the same with Espeon and Deoxys-EX, although they both have different strengths.
My suggestions would be
-1 Espeon
-1 Vaporeon
+1 Flareon
+1 [whichever Eeveelution that has the best matchups in your nearby meta that is at the count of '1' after changes]
Now the trainers.
-2 Frozen City +2 Training Center (HP boost)
-1 Ultra Ball +1 Skyla
-1 Colress Machine +1 Skyla (I honestly think Skyla is a bit more important to gather the tool you need).
Energy:
-2 Water Energy
+1 Psychic Energy
+1 Fire Energy
Possibly:
-1 Plasma Energy
+1 [energy that compliments best matchup] or Psychic/Water
Hope that helps!