Hi! Thanks for the suggestion. I just created another "test" user account, and AirDrop DOES work for it. I was able to send a file from my iPad to the "test" account on my iMac. Interestingly, when I'm logged in with the "test" iMac account, and I select AirDrop on my iPad, there are two iMacs that appear, one with the icon associated with my Apple ID, and a gray & white one presumedly for the "test" account (for which I did not enter my Apple ID). It is the gray & white iMac icon which receives the files fine.
When I return to my main user account on the iMac, AirDrop still does not work normally. HOWEVER, when I select AirDrop from the Finder sidebar (or the Go menu), I now AM able to send files to my iMac from other devices. I don't know why this began working when I created the new "test" account, as it hadn't worked before. It's certainly not the most convenient way to use AirDrop, and it isn't the way it used to work, nor is it the way it works in the "test" account, but at least I can transfer files. Clearly, as you suggest, some third party software may be interfering with normal AirDrop transfers (i.e. transfers that work anytime, regardless of which app I'm currently using, and don't require me to open up AirDrop in the Finder), but going through the process of elimination to find the offending party is not going to be worth the time, especially as I've now got a workaround solution.
Thanks so much for your help!