I am not certain about recycling concrete, but could just be unaware that that is possible lol.
As far as taking out concrete, I don’t think it is all that difficult. Hit it with a sledge hammer, then it cracks, hit cracks with sledge hammer, remove pieces, repeat. If you do get a jack hammer, you should be able to have this thing torn apart in an hour or so max.
We did this on our home this spring, and took all the pieces to the Fort Totten transfer station.
Depending on your physical abilities, and availability of a truck/SUV that is capable of moving this stuff to Fort Totten, I would say this isn’t a huge job. You would likely be able to find a DC resident on Craigslist who would run trips to the dump for you if you are unable, I know I have done things like that in the past, a Saturday morning should get the job done completely in my mind.