The MCC & JAR ATPL exams are meaningless here. As far as the FAA is concerned you have an ICAO CPL & ICAO IR. Nothing else.
If you have the hours for an FAA ATP then your best option is to do that. The FAA ATP includes an integral IR so only one exam & flight test ('checkride' in the US vernacular). If you're doing a type rating you can usually include the ATP specific items in the type rating checkride, thereby gaining both things in one hit.
Compared (UK flight tests) you can expect a rather thorough grilling from the check airman when you do the flight test. You'll be expected to answer operational scenario type questions at the level of the licence for which you're being tested. The ATP flight test is more or less an instrument rating flight test but using tighter tolerances compared to JAR eg quarter scale deflection for approach tolerances instead of half scale, similarly tightened with altitudes etc.
On the plus side, you'll find the (single) theory exam to be relatively easy. The bit I found most difficult was the rules & regs because they're so foreign. Don't forget the US uses TERPS and not PANS-OPS, statute miles for vis etc etc. Also the flight test is usually done using 'pop up' requests for approaches and not using an IFR plan & route. That *can* make things easy when it's quiet, but if really busy you can find yourself wishing for a nice long route sector!