AAIGUY is right. It's a two-fer deal (well, not really, it will cost you about $30 more). All you need to do is get your FAA ATP written done (this will cost you less than $100), get a US Medical, and then go for the Type/ATP ride. As soon as you get your permanent licence from the FAA, you can have it pegged onto your Canadian one by filling out the form and contributing $30 to "The Receiver General for Canada"
(5) Credits for Foreign Applicants
(a) Qualifying Flight Requirement
(amended 2000/09/01; previous version)
The holder of a licence issued by a Contracting State shall be considered to have met the qualifying flight requirement specified in 3(c)(iii), 3(g)(iii), 3(k)(ii), and 3(l) above provided the applicant has acquired a minimum of 10 hours pilot-in-command flight time on the appropriate aircraft type during the 12 months preceding the application for rating;
(amended 2005/06/01; previous version)
(b) Pilot Proficiency Check Requirement
The holder of a licence with a two-crew type rating issued by a Contracting State shall be considered to have met the Pilot Proficiency Check requirement specified in 3(a)(iii), 3(b)(iii), 3(f)(iii), and 3(g)(ii) above provided the applicant has acquired a minimum of 50 hours flight time on that aircraft type during the 12 months preceding the application for the rating.
(amended 2005/06/01; previous version)
(6) Credits for Foreign Flight Test
(amended 2005/06/01; previous version)
(a) The qualifying flight requirement specified in subparagraphs 3(c)(iii), 3(g)(iii), 3(k)(ii), and 3(l) above may be performed under the supervision of a qualified person who is licensed by a Contracting State provided the applicant submits a letter from the State’s Licensing Authority, or other source acceptable to the Minister confirming the personal log entry, and the qualification of the person who supervised the flight;
(amended 2005/06/01; previous version)
(b) The Pilot Proficiency Check requirement specified in subparagraphs 3(a)(iii), 3(b)(iii), 3(f)(iii), and 3(g)(ii) may be performed by a person authorized by a Contracting State provided the applicant submits confirmation from the State’s Licensing Authority, or other source acceptable to the Minister confirming that the applicant meets the State’s skill test requirement for the issue of the type rating.
(amended 2005/06/01; previous version)
Regulatory Source 421.40
Here is one training company in Phoenix, Arizona:
K & S Aviation