Went to pick up some copies today and the answer to my monitor-recycling problem was right in front of me: Staples stores will recycle your used "computers, monitors, laptops, and desktop printers, faxes and all–in–ones" in exchange for a $10 transportation fee, according to their website. Smaller gadgets and peripherals such as mice, speakers, and cell phones can be recycled for free.
The unloved objects are processed securely by electronic waste giant Amandi Services, about which I was able to learn very little except that it's huge and has been around for a long time. Do they send computers to China to leach toxic waste into poor people's lives? Possibly. Is it better than my solution of leaving my monitor in the Dean & DeLuca dumpster? Most likely.
Now if only someone would just design a monitor that a) lasted longer and b) didn't create toxic waste when it finally croaked.