This is the T-motor in the ex-power station yard in upstate New York, which has been discussed repeatedly on RyPN and is well-known to the locomotive preservation community. A major issue is that access to the locomotive is extremely difficult; another major issue appears to be that, in part due to its chassis design, the locomotive could not be hauled on its own wheels in train in its likely current condition.
If I were going to move it, I'd need to coordinate a service like Hulcher to do lifting and positioning, and build cradles to hold the two half-running gear assemblies and the carbody separately. These would then be secured to either flatcars or heavy-load trailers (like Silk Road's) once you got them effectively across the active adjacent main and yard, and transported -- naturally avoiding humps, and following routes with stack overhead clearance where possible.
At the arrival point, the underframe would be removed to its own track (and probably left separate while being refurbished). I would mount the carbody on span beams at either end, "permanently" supported on adjustable screw jacks well outboard of the track underneath, allowing easy reassembly or 'wheeling' of the locomotive once the carbody and running gear were all restored; this relieves any particular need for cranes or special handling skills after the initial unloading operation. (You will need some method of handling the jacks and beams, but even comparatively small hydraulic cranes should handle this.)
An important consideration is that the locomotive is not 'free for the taking' and if I recall correctly a large number of serious preservationists would strongly oppose removing this or the other ex-NYC locomotive from the Northeast, particularly to a location far removed from any existing preservation shop or volunteer base and with no more than 'shoestring' financial arrangements in place.
At a minimum, have the full amount of money needed for all the expected move costs plus renovation, physically on deposit 'in the bank,' before even calling around to see who would help donate equipment or money when the time comes. And be very, very careful making 'connections' or discussing motivations with existing museums or people in the preservation field, as they have long and very wearying experience with certain people and personality types, including those that fit the hackneyed old genus 'foamite'.