I think I have it figured out.
Kind of like you suggested in #3.
I created attributes in SessionVariables to hold the Client's Names, DOB, & Gender.
When they want to create a new client, I present them a SessionVariables form, with those attributes on it. It looks almost identical to the normal New Client form.
The Save button calls the Potential Conflict Query.
When they close the Query, if they choose 'Continue', I then just do a CREATE ClientMaster and update the corresponding attributes for each SessionVariable attribute and present the normal Client Entry screen. If they choose Cancel, it just ends the process.
Then it is just a matter of them deciding if they want to continue entering the new client, or closing it without saving anything.
It works, and is only slightly different than their current 'Magic' program.