Ok, thank you for the clarification, so this just means a pilot who's built their experience in Europe cannot upgrade to captain until they fly 1000 hours in the US with a part 121 carrier, right?

Which I guess is a requirement at most regionals anyway and will never happen at any of the majors. I just want to make sure if I commit and pay $13k to convert my licence and 737 rating, I won't be caught out by any technicalities.