To build the hours in the USA I understand that I will need the Multi Add-on to my FAA PPL. Is this correct? Or can I get my JAA Multi converted and added on to my FAA by way of a paperwork exercise without a course and visa etc? The cost for the hours where I currently live and work will be 8750 euros (or 7000 pounds sterling).
If you have a US Restricted PPL based on a Foreign PPL, yes you can add the foreign ME rating to the license.
If you hold a independent US PPL (You have done a check ride with a US examiner) then no, you cannot add a foreign ME rating to a US license.