The information in post #2 is a reasonably complete overview of the steps needed to obtain a US private pilot certificate using the modular method which is appropriate to your needs. I am doubtful that a restricted US private pilot certificate could be issued on the basis of your foreign licence because it does not confer at least private pilot privileges. That is a question for the Foreign Verification Department in the Airmen Certification Branch in Oklahoma City. See contact details
here. Otherwise, post #2 assumes the dual flight instruction you have received will be credited by the FAA towards US pilot certificates and ratings. The provision on crediting is in section 61.41. You'll find that and all other regulations covering US pilot certification in part 61 of title 14 of the Code of Federal Regulations, available online at ecfr.gov. There are additional provisions in part 141 for training courses taken at non-collegiate vocational pilot schools or some collegiate aviation schools. Part 141 training courses will probably not be appropriate to your needs owing to the experience you have already gained.
The FAA does not issue multi-crew pilot certificates. A brief summary of US pilot certification as it contrasts with European licensing is given in pp 32–35 of
GAO-12-117,
Initial Pilot Training: Better Management Controls Are Needed to Improve FAA Oversight. Specifically on p 34:
FAA has not developed regulations for a multi-crew pilot
certification, and there are differing views on its usefulness and necessity
in the United States. FAA officials said they have been studying the
feasibility of implementing the necessary regulations for U.S.-based
commercial airlines, but they also indicated that U.S. airlines have not
publicly shown interest in a multi-crew pilot certification due to the
availability of a broad pool of commercial and airline transport pilots in the
United States. Representatives from three regional airlines and one
industry association told us that, with the number of furloughed pilots as a
result of the economic downturn in 2008, application of the multi-crew
pilot certification is not needed in the United States and would be too
restrictive in nature. The certification would limit pilots to being first
officers, limit them to a specific aircraft type, and not allow them to
transfer to other airlines. Traditional pilot certificates require more training
hours, but do not include such restrictions.
See also p 11 et seq for a review of the different types of pilot training schools in the US. The FAA itself does not require pilot training to be conducted under the auspices of a pilot training organisation. Were I in your position my next step would be to set up a spreadsheet mapping the experience requirements for the various US certificates and rating, line by line, to the appropriate entries in your personal flying logbook. Note the US definition for the term "cross-country time" in section 61.1.
There is probably an alternative route via Canada should the FAA will not recognise your MPL training time in accordance with section 61.41.