This I can agree with. The and would be GREAT Fulton Local services and would allow the to run express to Lefferts. As for the Transit Museum in this case, I'd move it to the current Long Island City station used by the LIRR where you'd have to build a 2 or 3 floor building to store all of the artifacts and you'd have to consider sea level rise as an issue here if you want to relocate the Museum (which is what this proposal is doing). Anyways let me get a few Questions out of the way.
How are you going to move all of the Museum trains into the Subway System?
LIRR of course (the Main Line though) I don't think subways are allowed in Lower Montauk. Of course the only way for this to even be a possibility is to build the Queens Bypass or the extension to Rochdale/Laurelton/Rosedale.
What's the point ?
To allow SAS to run Local via Fulton. Isn't this the whole point of the proposal. Also one benefit is that you'll attract more tourists that way since it is now closer to Midtown, and since @RR503 mentioned ENY Redevelopment. I go to school in that area so seeing redevelopment would be nice (I know that they're building a new school in the area and it'd be better if they built an apartment complex near Crescent St which would be next to this new school. Don't believe me, go see for yourself.
What happens to the artifacts?
They get delivered to this new museum via truck, train, or whatever is best for them.
Will the Long Island City (LIRR) station close down?
NOPE. That would be pointless. Besides, there's a ferry one block away. Only 2-4 Tracks would be reserved for this new museum. A building can be built on top of this reserved trackage which would be this new museum. The Long Island RailRoad would keep the remaining Trackage and will have a "proper" station since that area BARELY looks like a station. Besides, Long Island City, Greenpoint, and Hunts Point (Queens) is going through some really nice redevelopment, so it would be logical to relocate the transit museum.
How will people know about this new museum?
Simple. Just advertise on the , , (LIRR), and the Nearby Ferry.