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If you get a Multiengine Sea ATP before your ATP written expires you're good to go. If you get a Single Engine Sea ATP you'll have to complete the CTP and pass the new multiengine ATP written before you can be issued a FAA ATP with a multi class rating. You could also do the ATP in a Barron or PA-34 and then add the Gulfstream ratings later.
VC-10 Tail
They only allow simple calculators with no memory. Phones are not allowed in the testing rooms.
I have no idea what is involved in a MCC or jet conversion class. The CTP can be done in whatever sim is listed in the Training Center's authorization. I know of a TC using RJs and MD-80s and thinking of adding 744s.
If you find a TC using a type you are rated in it would be between you and the TC to see which sim is used.
I've never heard of the CTP being called the FAA Multiengine CTP and searching for that term doesn't bring it up. However since it is required for a FAA ME ATP I can see where people might call it that.
The sim training outlined for the CTP and the maneuvers normally required during a recurrent class only overlap in a few areas so I don't think anyone will count it as recurrent.