The bottom line these days is train where you want to work, as long as you can work there. So called conversions are messy. To even start converting your basic FAA Multiengine/Instrument/Commercial ticket You'll need to have 100 hours PIC, which in EASA land practically means solo time, so that usually means going back to do an extra 50-70 solo hours or thereabouts, the only upside is that it can be single engine time. Then you'll have to fork out for an official study package and study for and pass all 14 ground exams. After that you can expect to fork out for anything from 20-100 hours instrument and commercial conversion training, much of which will be multiengine instrument time at European twin engine prices, including all the extras you have to pay for such as ATC fees, marshalling, parking, "handling", high fuel prices etc etc. I've heard of some people pretty much doing the entire instrument training from scratch, whether this was necessary or not - I have no idea.
The new competency based Instrument Rating conversion requires 100 hours Multiengine PIC IFR time to start with. That's 100 hours solo (in reality) multiengine actual IFR time.....some people take years to log that. So it's not much of a concession to anyone but a well seasoned Instrument Rated multiengine private pilot. Even then they need to do a certain amount of conversion training because things are done differently.
So that's my view, train where you want to and can work, it's the way things are set up now and they'll get their pound of flesh out of you one way or another. I wish I'd done the same.