Wait, 6 Alakazams without Recover, Reflect, or Light Screen? Piece of cake.
Get 6 Chanseys, each with Softboiled. Give a few of 'em Thunder Wave to disable, Light Screen perhaps for an added boost or even Minimize, Ice Beam and/or Thunderbolt for damage. Thunder Wave each Alakazam when they show up and pound away.
Honestly, those Alakazams would be better off if they had Recover, Reflect/Light Screen, and Thunder Wave too. Psychic and 3 other less impressive attack moves is a terrible setup, especially when all 6 have the same moveset and you'd probably just be using Psychic on everything anyways due to its strength.