Would contracting amtrak long distance trains out to a private railroad save money? if yes then how?
Save money for who?
A lot of this restructuring stuff is window dressing, it's about stealing from Peter to pay Paul.
So if somebody can make their own budget look good by offloading costs onto somebody else's budget, and if people are getting praise and bonuses for making their budget look good, then these things wil happen.
I could actually see the case for contracting out the operating crews, at least for large portions of the routes. Having to staff a bunch of crew change points with conductors and engineers, making sure to have an extra board deep enough to cover those who are sick/on vacation/etc., any overhead needed for having the specific locations up to the standards needed for an office, etc. all for a single train each way each day is pretty inefficient. Having the freights handle the staffing and location concerns could let their economies of scale in that area work to make that staffing less expensive while still ensuring proper staffing (it's a lot easier to account for sick/vacation leave and overhead expenses when it's spread across a hundred or more employees running numerous trains a day than it is to account for that for a dozen or so employees running one to two trains a day.)
I don't see the proposal up currently as having any bidders, though. From the sounds of it, they need both the trackage rights and the cars to make it happen. The Class I's don't have the cars to make it happen (nor do they want to deal with that) and any private railcar operator will likely have a difficult-to-impossible time working with the Class I's for trackage rights.
I could see contracting out the engineer position's back to the host railroad, but not the conductor's, who must be knowledgeable of all passenger related matters, besides the passenger cars.
One of the benefits of Amtrak taking over the conductor's years ago, was the elimination of the Chief of On Board Services position's, since now all conductor's were "passenger qualified", with the necessary knowledge to supervise OBS employees...
There is not much difference operating a passenger diesel from a freight, other than the Head End Power system, and somewhat higher speeds...