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Replace RNG with builder mechanics. Big power requires investment; change things like RNG status to guaranteed status if the move is chained like Rollout or used in combination with other moves like the pledge moves. Change the "haha, skip your turn" mechanics to something else entirely:
Paralysis halves speed; target cannot use defensive or recovery moves like Protect, Ally Switch, Recover, etc (it would be a long list, but the moves would all share that theme).
Sleep reduces speed by 90% but receiving damage will instantly awaken the target (lasts a fixed maximum of three turns). Rest still puts its user in full timeout for 2 turns.
Confusion halves SpA and applies a 25% recoil damage penalty to all attack moves.
Frozen applies a -3 priority to all moves.
Attract lowers ATK by 1 stage (initial move effect) and then applies a Truant-like effect.
etc, etc, none of those are particularly serious, but the gist is to give things counterplay without entirely ruining anybody's ability to actually play the game.