While in most cases I am a huge voice for doing it yourself, the cooling system is something that having it professionally done is worth it in the long run. And that is simply because of the time that it takes and the fact a professional flush can do a much better job in cleaning out that gunk you speak of.
I have done coolant flushes myself and the heat up and cool down cycles are time consuming, you need to drain the radiator, pull the lower hose and pull out the front knock sensor to make sure your getting as much out as you can, then you have to repeat all that a few times to get it done right.
A professional flush can be done with the engine running and they do a good job of cleaning out the system. $70 is a pretty decent price for it being done at a dealership. I had mine professionally flushed and I think I paid $85 and that wasnt at a dealership and if he can back flush it and clean out the heater core, I think that is a decent deal.