Wildman -
You should change the sets to a CLS of POA (Privacy Override Allowed). No action is required by the users, the second set will automatically be allowed to pickup the active line.
Not sure if this will solve the Feedback issue (never called the person next to me on the speaker phone)..
If it doesn't - you may have to do something kinda 'funky'...
Leave both sets with CLS of HFA - Turn one sets speaker volume all the way up (so that the room can hear the conversation) and turn the others speaker volume all the way down.
If you still get feedback - then you will need to 'physically' disconnect one of the speakers.....
Chas2002