You would still have to do a checkride in the EASA system to convert the ME and IFR ratings. You may not have to do aclime flights but will find schools are somewhat arrogant and dubious towards FAA pilots so would want to fly at least a test flight with you to check skills prior to putting their reputation/pass rate on the line with the local CAA. But in the grand scheme of things.. whats the cost of a few hours extra in the twin..
With your hours you at least wont have to do any writtens to convert the FAA instrument, but just have a exam oral with the examiner, so no rush to get ATPL writtens out of the way initially (as the ATPL covers all 3.. ppl,cpl&atpl easa theory)
But as you need an EASA ppl to start CPL modular training anyway, this is likely your pathway to an easa CPL.. intergrated is waste of time these for a person like you as its wasting money doing all the same stuff again