Jesus H phucking christ, what a rip off, that is one of the most padded quotes I've ever seen.I'm kinda thinking that I should do this, as 3/4 of this work is (profit for them, but also) things to fix the flashing, etc. that are independent of the reinforcement work.
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If you were going to do it yourself I would estimate your cost be much much lower,
Concrete would be under a grand, no need for a pump if you buy a midmixer, materials would def be under 8k if you shop right, dumpster rental would be 800ish, I bet you would be in the 10-13k mark if you didi it yourself if you have the tools, and know how.