I have been in the same situation
I have been in the same situation as you although it was back in the 90's so maybe things have changed since then - I don't know for sure.
I contacted the CAA for an assessment of my experience ( FAA ATPL plus approx. 6000 hrs ). I was exempt the navs and just had to do the techs . Did that and contacted Mike Smith at Heliair about the flying side of things. Mike being Mike , thought I shouldn't have to do any thing at all considering my experience . A couple of weeks later he called and said as long as I had more than 50 hrs on my FAA ATPL I was entitled to a CAA one !!!
So of I go to Gatwick to demand my ticket . Spoke to Ron Jenkins who confirmed everything !!!!!! As you have to have type ratings on your licence in the UK ( unlike the US ) I just had to do an hour of general handling in the aircraft of my choice ( B206 for me ) and Hey Presto , one shiny new CAA ATPL was on its way to me.
A result from the CAA !!!!!
Sorry I waffled on so much , this will make good bedtime reading along with CRM notes . It's probably all different now what with JAA and multi - engine requirements but it may be worth a try. It still makes a good story though , and it has a happy ending 1