Still not equivalent then. You hold a *Commercial* licence + IR + ATPL theory. You can be legal PIC in public transport operations, but you are limited to PIC in single pilot aircraft. No different to the holder of an FAA Commercial licence + Instrument + ATP theory, for all practical purposes, so that's what you're equivalent to. The whole 'frozen ATPL' language is nothing more than a European (well, it started as a UK thing, I seem to recall) shorthand for CPL+IR+ATPL exams. In recent years it has broadened to often include MCC as well. I also think I remember it started as a marketing & advertising ploy by the CAP509 (integrated, in JAA speak) schools, as a way to improve the perception of what they were selling. I saw it start to happen in Australia too. The idea is no different to someone with a PPL & passes in CPL theory saying that they have a 'Frozen CPL', or a student pilot with passes in the PPL exams having a 'frozen PPL'.
If you're serious about a move to the US - or anywhere away from the European terminology - I strongly suggest you use the correct name for your qualifications. 'fATPL' is a meaningless term here and leaves the impression you're trying to deceive about what level of licence you actually hold. Bear in mind that your ATPL exams & MCC aren't worth anything in the US (except your understanding of the theory will be rather better than a typical CPL candidate here). Only the licence you have been issued counts. Which, by the way, is no different to some one trying to get credits for their ICAO licence(s) to get a UK/JAR/EASA licence. It's much easier going from ICAO to FAA than ICAO to UK/JAR/EASA, though.
If you go to
FAA: Home and look for the links to the regulations you can find exactly what hours you need for an FAA CPL & an IR. Pay particular attention to how the cross-country time is defined for each licence & rating - it varies! Part 61 of CFR14 (often referred to as FAR61) is the section you need.
In fact, here's the link to Part 61. Definitions at the beginning, and the requirements for each certificate further down:
eCFR — Code of Federal Regulations