Moody doesn't seem all too broken to me in Ubers. The pokemon that get the ability are very weak and all except two (Remoraid and Octillery) are vulnerable to Aura Sphere, which ignores any evasion boosts and, while not learned by many pokemon, can drastically discourage using Moody. Sure, it could raise their stats to an annoying level, but so could any pokemon setting up that remains unchecked. Moody's stat raises are too random, and since it also hinders a stat each time, this can be taken advantage of early before any stat boosts raise too high.
Applying to Double Team / Minimize as well as Moody, pokemon can run Aerial Ace, Shock Wave and Faint Attack as well as the aforementioned Aura Sphere if they fear losing to such a risky strategy - they're low power but when fighting an opponent that relies upon evasion it can easily prevent a loss.
Mainly, the only problem with Moody I see is if Smeargle Substitute/Protects (and even stalls with Spore) and passes all the boosts to a much more powerful pokemon. This can be gamechanging, but to prevent such an event perhaps Haze on Darkrai, or Clear Smog on something like Gastrodon if the opponent lacks a Substitute, could be used to negate the boosts. Other moves like Perish Song work as well.