As reported about 5 weeks ago, Metro North has found a way to get Amtrak locomotives through the Park Ave. tunnels, by using tracks that do have some side clearance. While it may now be a lost art, long ago it was possible for Amtrak employees to be trained and qualified on new territories, like the route to Grand Central.
So to summarize the issues pertaining to Amtrak moving Empire Service to GCT:
1) Amtrak P32 Issues: 3rd Rail Shoes, No Forward Escape Hatch
2) GCT Slots and turning availability (unless cab cars are used for push/pull)
3) MNRR Crew Availability
4) MNRR P32 Pool Availability (to mitigate problem #1)
By rough count, it appears there are a maximum of 26 unique Amtrak trains /day which run between NYC-Albany in either direction. That would be a lot of capacity that would be taken off-line in the event these trains are precluded from entering NYP (due to trackwork) and GCT (operational challenges). Replacing with buses probably would not be feasible given traffic and capacity required.
Perhaps the best option is to transfer at Croton-Harmon and have MNRR run a special into GCT. Based on timetables, the ride in from CRO on an express is ~:50, possibly ~:45 without stopping at 125th. The transfer would be an inconvenience, but probably is the 'least worst' option given the other outstanding operational challenges. This of course presumes MNRR has the equipment and slots to accomodate these specials.