First of all, Patch is not about how many healers do you have, it's about how good your healers are. You can try it with 7 healers but it won't make any difference and it's useless. While healing hateful strikes, it's all about how fast your healers can heal OT back to 100%. Go ahead and check your healing records, you will see at least 3 healers have more overhealing than actual healing.
My guild is doing patch with 5 heals max, and the fifth guy is resto dudu who is just backup if anything goes wrong. 2 hpalas, shammy and a disc are enough. Your raid just needs to use all the skills they have, like multiple innervates, priests' hymns, shams mana tide, not to mention mana potions. Quality over quantity.
Same goes for Noth. Why the heck would you force your OTs to tank 2+ or 3+ champions? Not even most skilled prot palas would survive that. Again, use your full raid, not only your tanks and healers. Have your spriest always keeping 1 champion shackled, have your hunter(s) using their freezing traps, have your shamans use mass aoe root totems, have your druids use actual single-target roots. MT should always focus on taunting noth when he comes back.
Anub- have your hunters use misdirect when scarabs spawn, as well as rogues using tot.
Same goes for other bosses. You will find naxx quite enjoyable for raiding once your raiders stop tunnelvisioning and just dpsing the boss instead of using their skills and abilities to their full potential.