I don't know what an interlocking is, but I would say that's a likely reason. If I try and go from DC to Raleigh on that date I can choose from the Carolinian and the Silver Star. If I change my destination to one stop further, in Cary, my only option is the Silver Star. If I go one stop further to Durham, Amtrak says maybe I should travel on Friday. There are some lovely trains going to Durham on Friday. I hope you will give some serious thought to Friday travel.
If you reverse travel, Raleigh to DC is fine except you have to take a bus to Rocky Mount to catch the Silver Star. You can also catch that bus in Cary, but there are no provisions for the Carolinian. And if you wanted to start in Durham, it won't pick you up until Friday. The Piedmont, which usually runs twice a day between Raleigh and Charlotte, only has the early morning run.
It all seems consistent with idea that somewhere in the Raleigh/Cary/Durham area the tracks will be unavailable after morning.