I believe that Ualaa used to run a 5 man healing team for AV and things, and he had tweaks like swiftmend on round robin. You certainly don't want to step into any raid with four just 90 healers, but I'd suggest brainstorming a little the strengths of what you are bringing (won't waste more than one tank cooldown at a time, for example, a stack and forget him lifebloom rotation on tanks) and take your toons into LFR in pairs as they gear up. Getting anyone to let you four box in a normal raid is probably not a realistic goal. You might find a boxer that hates to heal that wants to do flexes though, once you've reached a 540+ ilevel.

I don't raid while boxing (although I do take five toons to ordos groups), and I think most people that do probably use disc priests or monks for good passive rotations.