There is no MPL in the FAA arsenal, and, apart from Transport Canada, no real ‘conversion’ process. The FAA allow you to apply for an ATP with a foreign Commercial certificate or higher, but it is the standard application process. You can start the application in IACRA, which now includes helpful error-checking.
You should be able to take your ATP check-ride combined with a Type Rating - if your current type is available here (recommended). This should give you MEL class and type.
As for completing the requirements, you will need to tick all the boxes for the components of 61.159. This should not be a problem if you hold an EASA ATPL.
Finally, you will also need to complete the ATP-CTP course, before taking the Knowledge Test.
Good luck.