All I can tell you is that if the host railroad has a scheduled track outage where and at the time that Amtrak operates or is scheduled to operate, the work is planned in advance, and if the decision to hold Amtrak trains for an open track would severely delay that train, and if the host railroad has an alternate route of equivelent capacity and quality to detour the train(s) in question, then by contract Amtrak has with the host railroads, the host railroad is required to provide full assistance to at least attempt to detour the train. This, however, sometimes does not happen, for internal reasons associated with Train Management.
The main reason you will see an Amtrak train detoured, especially a Long Distance train, is because of equipment turns. The equipment has to get to the other end to be able run a train in the oposite direction. If you stop a train at a point outside of a major terminal for that train, the intermediate point is usually not equipped to service, inspect, fuel, stock, etc. that equipment.
A class one main line will usually be maintained to high class standards. This is where you will see the detour Amtrak train. You usually won't see one detoured where the speeds are somewhat slow, but the exception is when #7 & #8 were detoured from Tunnel City Wisconsin to Chicago, mostly over UP Lines last June. I for one, still couldn't believe that they did that too!
As far as training crews for detours, in certrain cases, the host railroad will qualify certain Amtrak engineers for extended detours. A prime example of this was in the later part of 1999 when UP was doing all day track work on the Fresno Sub. between Stockton and Elvas for several months. The (back then) one daily roundtrip Amtrak San Jaquin that went to Sacramento was detoured over the Sacramento Sub. around the work and UP qualified the regular and extra board engineers on this segment. In a case of a detour of only a couple of weeks, like is going on with #5 & #6 between Alazon and Grant Tower (in Salt Lake City) it is cheaper for UP to provide Amtrak with a "Pilot" crew to run over this segment because it only of a short duration.
Hope this answer most, if not, all of your questions.
As an old SP crew once told the dispatcher, "Hey Dispatcher, here comes the Hooterville Trolley!"