Hi Natterjack, The FAA defines a cross country anytime that the distance from the departure airport and destination airport is 50 NM or more. You can combine the ATP checkride with a type rating checkride. The only book needed for the ATP written is a Question bank book, like the one Gleim publishes.
How do you plan on doing the conversion?? The regs would only allow you to get the a FAA CPL IR, since those are your JAA qualifications.
Be aware that the FAA may require you to do the FAA written test for your instrument rating. To be able to get a standalone FAA ATP you need to have had a previous standalone FAA certificate. Anything that says "based on a foreign certificate" is tied to the expiration date of your JAA license.
As you can see, it is quite a tricky situation. The information above is just a rough summary. For further details pm me.
Happy landings, TG