A quick update - having Danielle (Spinarak, now Ariados) beat Whitney's Miltank was actually pretty easy - all I needed was a Reflect up from the previous battle and was eventually able to poison-stall it to death.
Managed to eventually find a Pineco in Ecruteak City, and Detonator quickly joined the team. Then made it out to Route 39 and caught Melville the Tauros, who is quickly becoming a powerhouse.
(At the moment, he's annoying the hell out of Morty's Gengar with a moveset of Rest/Horn Attack/Scary Face/Pursuit. Gengar doesn't have Curse and only has Shadow Ball and Sucker Punch as attacking moves, so I spammed Scary Face until it ran out of Sucker Punches. Now it can't harm Melville in any way, so it has to wait around and try to keep sleeping me until it dies/runs out of PP. This is quite a bit of fun.)
When I finish the Morty fight, I'll be able to use Surf and will finally be able to finish my team with the addition of Clause the Psyduck! Psyduck is only available surfing, but I've got Temp the Wooper Surf slave to cover that for the moment. (EDIT: Durr, forgot Dratini and Tauros can Surf. Guess I won't be needing that...)
(EDIT 3: Clause has Damp and a +Speed nature, so it's Shadow Claw and Screech, with no Amnesia allowed).
Current team:
Manly (Bayleef) - Lv. 26
Amelie (Dratini) - Lv. 23
Danielle (Ariados) - Lv. 22
Melville (Tauros) - Lv. 19
Detonator (Pineco) - Lv. 17
(I know Ariados is supposed to be my lowest level, but Tauros and Pineco are recent catches and I got bored grinding them up so I went to the Gym. That'll be fixed ASAP.)
EDIT: TLK, take the Eevee that is given to you and evolve it into... whatever you want! The Eeveelution may not have any STAB attack with more than 40 Base Power and must be your lead Pokemon against every member of the Elite Four.