The FAA ATP written exam (one, not fourteen) is very simple to study for and pass. From what I remember of it circa 1980 it had Air Law, Weight and Balance, Systems, Performance and Meteorology, just 5 areas.
You can use one of many self-study options available and, thanks to the Freedom of Information Act you can even get a copy of the actual test questions. (When I did the test there were about 900 of them, divided into those 5 categories, and there are only so many questions you can ask about, for instance, W&B. Systems, on the other hand, was based on the B727 and I am sure that has changed and moved on.) I used a combination of a programmed-learning course and plowing through those 900 questions.
When you are ready (about a week will do the job) present yourself at one of the many testing centers to do the test on-line with very little advance notice. (Remember to take the study materials along to show how you made yourself ready for the test.) After that you just need the written confirmation of the test results to hand over when you do the practical test.
Under the FAA you do not need experience in large aircraft to hold an ATP. You just need the minimum experience to take the practical test, when you are then issued your ATP. The practical test is very similar to that for the IFR with the only additional consideration being CRM, since an ATP holder might command a multi-crew aircraft.
I think that is basically it but I am ready to be corrected in any of this by those more up-to-date on the doings of the FAA.
The real problem with the FAA licence is that many places do not accept it, perhaps because it is relatively easy to obtain.