Beuker,
It's not actually a conversion. Your existing experience counts towards the rating and/or certificate.
Does your FAA private pilot certificate include an instrument rating? You can get a commercial certificate w/o the instrument rating, but it is very limited. Is your private ticket based on your EASA PPL? If so, did you do an instrument rating the same way? If yes, then that instrument rating doesn't count - you need a "real" FAA one. When you finish the commercial, you will have a "real," independent FAA certificate.
Do you have 250 hours of flight time? With your EASA CPL/IR I would assume so. An FAA commercial certificate requires 50 hours of cross country flying - to an airport at least 50 NM away. Also required, but can be part of the 50 hours, are some specific longer flights. One must be 350 miles. One is 2 hours and 100 miles day time and ditto at night.
You need:
Medical
50 hours XC flying as above
Instrument rating (training, written test and practical test)
10 hours in a complex airplane if you don't already have that
Training in the FAA-required commercial maneuvers - nothing like what is done in Europe
Written test. Practical test.
If you get with a good instructor you can help reduce expenses by overlapping multiple requirements - you can do an instrument cross country in a complex airplane at night... Fill in the gaps with smarts not money!
I believe that you have to be an actual resident of the US to use a Part 61 school. You need a visa, but maybe not TSA. Hmmm. TSA is required if you need an instrument rating.
Regardless of which school you use, DO NOT PAY THEM A LOT OF MONEY IN ADVANCE!
Many people have done this; you can too.
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Terry