it seems that if one wants to dispose of a large collection - unless one is willing and able to piecemeal them on ebay, then the best bet would be a record store-of which there are less and less that can and are willing to take them, and/or afford them. In my experience, libraries are not interested anymore. Radio stations may be able to accept some, but there are few of those left that even play LPs anymore. My guess it that a good majority of those would end up in the private collections of the DJs / interns. In Chicago, Dusty Groove would take the A+ items and nothing more, but give you pretty good money, Groovin' High would take a few more and a little less money, and Jazz Record Mart would take them all because they are less discerning, and can afford it space-wise and $$ wise. They would give you a lot of money for the good stuff and not much for the B and C stuff. All 3 would probably send someone out to your house to peruse. as far as the other stores in the Chicago area, I doubt most would be able to absorb / afford 10,000 LPs, most being rock oriented stores, with little / less interest in "jazz". Another idea; some public radio stations have fund raisers - physical events where people donate items and the proceeds go to the station. You could donate all of them and take a healthy tax deduction, and feel good about a) getting the items in the hands of like minded jazz fans, and b) helping out for a good cause. The only down side to that is that a lot of them would probably end up in a volunteers' collection.
hope this helps...
and good luck,
Elo