Hi larryr1,
My wife and I have been sharing the same Apple ID since iCloud was launched. I too want to resolve the AirDrop problem without giving up our shared Apple ID.
I have been reading this thread backwards and just got to your post which explains resetting iMessage and FaceTime. This is what I have under Settings/Messages/(Send and Receive) on my phone.
Apple ID: <shared Apple ID>
YOU CAN BE REACHED BY IMESSAGE AT
<check mark> <my phone number>
<check mark> <my email address, (shared Apple ID)>
<not checked> <icloud.com email address>
<not checked> <me.com email address>
How do I delete the phone number and email addresses? I can tap on the blue circled "i" against the email addresses and tap "Remove This Email". But, the phone number is greyed out and I can't seem to do anything with it.
Thanks!
PS: I just found these instructions "iOS 6 and OS X Mountain Lion: Link your phone number and Apple ID for use with FaceTime and iMessage" here http://support.apple.com/kb/HT5538 . There is a section titled "How to unlink a phone number".