We're already somewhat talking about that here:
CUOMO PROPOSED HIGH SPEED SYSTEM IN NY.
Basically, you need a new routing, off MNRR's Hudson ROW. Which is not a bad idea. Run it up the median of the NYS Thruway (I-87) on the west side of the river. The new TZB (#NotTheMarioCuomoBridge) has a provision for rail in the center of the two spans. On the East of Hudson (EoH) side continue it down the Thruway into the Bronx. To bring it into Manhattan, you could connect it at "BN" yard in the Bronx, do a little reversal across to Spuyten Duyvil and the Empire Connection (operationally problematic). A more elegant solution is a connection to the Hudson Line at BN as noted, but let it run into GCT. You're not talking about too many frequencies, so the short run into NYC on the shared EoH side shouldn't be that bad.
In Albany, maybe even use the old Union Station on the WoH side, and bring it back across to the EoH side on the existing Amtrak route to run it to Montreal through the North Country. Two extended Empire Service trains a day would do it.
And let Virgin operate it! How to pay for it? Increase the tolls on the NYS Thruway. Or for that matter, Virgin might be willing to do it with just using the ROW rights to the Thruway and overhead rights once on the Hudson below BN.
Okay, I know, what do you replace the EoH service with? An extended MNRR or NYS operation (MNRR only operates into Dutchess County by law) with limited stops covering the old Amtrak stops, with more LD type equipment. And contract it to Virgin
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You're killing two birds with one stone: Empire Corridor as far as Albany, and Adirondack.