I went 22-5 and decided to forego the last 3 battles as I reached my goal (1700) and didn't feel like gambling it (I got punished for getting greedy after reaching a rating I wanted in previous competitions :P).
This was my set:
Impish 76 HP / 180 Atk / 228 Def / 4 SpDef / 20 Spe
The spread is slightly modified from the excellent one R Inanimate suggested for this set
on Trainer Tower - I added quite a bit of speed for a better chance at winning the mirror matchup, and knowing others would invest a bit in speed for the same reason, I tried to speed creep further. This led to a crazy game against someone ranked 1721, as we brought each other down to about 5% HP, and I won a speed tie for the first time at the end to take the win, while we probably both assumed I had lost since they had won the speed tie every time thus far!
The set is nothing too inventive, I started with a simple Yawn / Protect / Last Resort, but I loved the idea of Laser Focus to give myself a chance against Evoboost and Charm / Baby-Doll Eyes, so I tried it along with Last Resort on Showdown and it worked really well. Having to Laser Focus every time before the Last Resort was annoying against offensive Pikachu since I relied on them not waking up turn 1. The odds were in my favour, but that made it more of a gamble than it had to be, so I ended up switching to Double-Edge, which I absolutely hated. The recoil worked against my bulk and gave opposing Eevees 2HKOs where they should have had 3HKOs. I downgraded to Return and never looked back; I had underestimated the power of the Adaptability boost!
I also made sure to breed a female Eevee since it has a overwhelming male ratio, in case some troll decided that Attract + Evasion would be a fun strategy. Surely, such person would have a female Eevee to catch the vast majority of male ones in the competition, so female seemed like the right call.
Autolosses for this set were Electric Terrain Pikachu (haven't met one in the actual competition) and Sub Pikachu if it was Light Ball Focus Punch/Z-move (also haven't seen any). Toxic Eevee was a bad matchup but I could win if they got the 3 turns of sleep (it was important to not Laser Focus on their Wish, but rather the following turn - the guaranteed turn of sleep - then Return on turn 1 of sleep, Return turn 2 of sleep, and Return again turn 3 of sleep for the KO).
Evoboost was not a great matchup but Laser Focus gave me a good chance; those with no bulk I had very high odds of winning against, and those with bulk I had decent odds if Crit Return + Return did enough. Yawn + Evoboost came down to sleep turns, and if I could get the same number of sleep turns as them or less, I could Yawn while I wake up and they attack, Protect the next turn, and then the field is mine!
In the competition, I won every mirror matchup (thanks to my speed, in my opinion, though sleep turns could have screwed me, so I got lucky in that regard), and every Pikachu matchup except for a Volt Tackle paralysis into full para the same turn - nothing I could do.
Overall, I really liked the set, I think its main strength was the fact that in addition to winning the matchups it naturally won, it gave me at least a fighting chance against most other sets and had few autolosses.
As noted by other competitors, the first day, I saw mostly Pikachu, some of them with the expected Z-Focus Punch, but also many random ones with the different signature Z-moves. The last 2 days, I saw only 1 Pikachu in 17 games, which goes to show Eevee was definitely the right call for this competition...!
Good luck to everyone who has yet to play their remaining games!