I've come across a couple stories where "back in the day" engineers would often speed to make up for lateness. (10mph+) How common was that? Does this still occur today?
Back in the day (when railroads operated their own passenger trains) it was fairly common.
Today, on the Class 1 carriers it is the next fastest way to lose your Engineers Certification Card - the only faster way is run by a Stop Signal.
Not only are their 'weed weasels' with radar guns, the data retained by the 'black box' data loggers gets reviewed by Operating Officials and prosecuted when violations are discovered.
I don't know Amtrak's procedures, however, I suspect they are similar to the other Class 1's.