Barcadi,
Firstly, having gone through the conversion from an ICAO CPL to a JAA CPL with ATPL theory, I can speak from experience and a number of years on have heard the stories of others having done the same route and I would have to recommend that you really think about which way to go. Personally, I'd save the money and complete all your training by the integrated method with one school that can give you a JAA license. Having done a conversion, I wish I'd just saved for another year and done it all here in Europe.
Once you obtain your FAA Commercial license and with the goal of converting to a JAA equivalent you will need to sit 14 ATPL theory exams along with of classroom work. In my case, this took about 10 months to complete as I needed to work during the time I was studying to fund the whole thing, plus I had to re-sit two of the exams. In Europe, most airlines require that you have completed the ATPL theory before you will be considered for a F/O position. Most schools will teach the ATPL syllabus in lieu of the Commercial theory.
You will also need to do 15 hours of Instrument time of which I believe 10 can be completed in an approved simulator. Once this is done, you will probably need about 5 hours of Multi time and I would say to allot yourself an additional 10 to familiarise yourself with the airspace and regulations where you will be undergoing your CPL and Multi IR skills test.
Once you pass your Instrument (10 hours x €140hr sim; 5 hours x €400 hr twin aircraft), Multi (maybe around 3 hrs x €400), and Commercial flight test (2 hours x €400) and have your ATPL theory completed (€2000 + €90 x 14 – test fees) (what is usually referred to as a Frozen ATPL) and have your JAA Class 1 Medical (€600) you will then need to complete an MCC course (€4000). These are all approximates of cost and hours required. So roughly €10 000 – which come to think of it is a lot less than I paid. Most would factor in about €15000 I think. Also factor in the time to complete all this and the cost of your accommodation and general living expenses.
I hope that is of some help.