Hi Jon,
Great question! This question does come up from time to time, but sadly, due to the way Conferencing works there is no method to configure the setup with a single button. The only thing that can make the process any quicker is to configure a Speed Dial button for dialing Live Record Pilot number.
From a subscriber phone, dial a called party
After the called party answers, press the Conference button on the phone,
****This is where the Speed Dial Button can be used**** and dial the Live Record Pilot number.
Press the Conference button again to join the Unity recorder into the conference.
http://www.ciscounitytools.com/HelpFiles/LiveRecord405/LiveRecordAppNote.htm
Hope this helps!
Rob