IMO, fighting healers should always be about reducing their healing (I'm thinking wound poison here) and interrupting heals (use Mind-Numbing poison as there are few instant cast heals - especially on pallies, so this makes the cast take longer, so you've got more time to kick). PvP against healers for non-healing classes is almost always an endurance question (and waiting for a mistake to capitalize on).
I would honestly concentrate more on steady damage so that you can get them down into burst range, rather than blowing all your CC options up-front and hoping you can make it to 0 before your CC wears off (or gets trinketed).
You've got a number of options at resetting the fight outside of the normal stun / silence moves - Cloak of Shadows should allow you to survive longer against a healer (as most healers are going to deal magic damage); Vanish will allow you to start a fight over and get another Kidney Shot / Cheap Shot combo, or another silencing Garrote. Restarting a fight is usually in your favor if you can start your opponent at less than max health and mana. Get in his face and Gouge him once your stuns and such have worn off and rebuild some energy / get a tick or two of recuperate.