I'm in a similar situation. My main is a BT raiding mage, and I have 4 alt 70s in various stages of gearing. Finding groups for heroics is ironically difficult given how geared out my guild is; everyone gets on to raid, but aren't very interested in 5-mans. It doesn't help getting a group together that everyone with a tank or healer raiding main wants to play dps on their off days. When we do get one going we tend to destroy the places, which I think they also find boring (I call it 'relaxing'). On top of all this, I'm up early on weekends, which is far from our normal raid times, and I'm very tired of doing dailies over...and over...

Multi-boxing seemed like a new challenge, so I recently started a 5-shammy team. 5 shammies can "solo" heroics once geared out, and so far I'm fairly easily able to clear all level-appropriate instances -- they're 37 now and currently farming SM armory. My thinking is when they're 70, I can sub out any other toon I want for a badge or drop farm run. Profit!

I'm kind of falling in love with the 5 shammies tho. They're just so awesome. I'm really liking multi boxing in general, except for the occasional "i'm gonna report you for botting" tells it's the most fun I've had since I started playing WoW.