Update #4! After discovering the evil organization that is Team Plasma and thwarting their plans twice (first in the Dreamyard, second when they stole a little girl's Pokemon), I decided to take a stroll in the grass before Nacrene City. Lo and behold, a sole Bliztle appeared. He seemed to have been separated from his zeal (a group of zebras is a zeal, look it up), so I took him in. Noticing his great similarity (read: none at all) to the King of Horses and the Steed of the White Rider, I decide to name him Shadowfax.
I trained Shadowfax a little so his level was on par with the rest of the team. I debated about catching an Audino I found, but then I was like 'fuck it, this is in-game, not competitive, I'd rather have his massive XP.' Once they are fully evolved, my trio could fit into a standard NU team.
By the way, this new restriction of having all my Pokemon 'Tormented' at all times was hard to get used to (I kept forgetting about it and almost violated it several times), but I seem to have gotten in the rhythm of it, especially with Blitzle (Charge + Shockwave is essentially the same thing as Shockwave x2).
I may be away from the internet for three or four days, so if I want to continue this challenge past Lenora during those days, I'm gonna need some more challenges! Come on people!
CURRENT TEAM:

Narcissism (Snivy) - Level 16
-Tackle
-Leaf Tornado
-Vine Whip
-Growth

Chimpaqu (Panpour) - Level 15
-Scratch
-Fury Swipes
-Lick
-Water Gun

Shadowfax (Blitzle) - Level 16
-Quick Attack
-Thunder Wave
-Charge
-Shock Wave