What sort of motor is best for continous high torque applications?

The motor shown in the video is a "universal motor". That type of motor has brushes and are normally used in hand drills and vacuum cleaners. They operate in a similar manner to DC motors. They produce good torque and work well with adjustable voltage controls such as found in a hand drill with variable speed.

Thus far that is all I can tell you with the information given.

Perhaps, try to find replacement parts for the sanding machine and maybe you will find the specifications that way.