You should install them yourself...it's actually both fun and rewarding! Many diys on this...and this is actually a reasonable one to begin with. Ask in your regional forums if anyone is around to help you.
But, $300 for a shop to do this work and bleed brakes isn't bad really. There are things that can go wrong on any car work...that wouldn't be the shop's fault. But, brakes are pretty straightforward.
As for labor cost doubling because you bring in the parts...seems a bit high...but there are reasons why you want a shop to order your parts. One, if there are parts' issues...the shop will fix them no cost to you. Second, they make money on parts...so at least they were honest enough to tell you they double labor rate!
If you read about 3 hours of brake diys, I bet you could do this...might cost you a little in tools if you don't have the right ones, but they'd pay for themselves in this one job alone.