It looks as though you have your answer, which is that you may renew a JAA medical in any country that has an approved AME. I have renewed my UK ATPL (non JAR) in France, Cyprus and Australia each time with no problems, just check with the AME before yur appointment that they have the forms.
Here is a link from the UK's CAA SRG website that will help you find an AME:-
http://www.caa.co.uk/application.asp...plicationid=21
And here is one that will help you find an FAA approved AME:-
http://ame.cami.jccbi.gov/