typically on the east coast they are called harescrambles, on the west coast hare and hound. I'v raced many east coast hare scrambles and have ridden one hare and hound course on in Utah, but never raced a hare and hound. In my (limited) experence the hare and hound is more of a high speed dez race while eastern harescrambles are tight woods.
As for a shorter harescramble race - they are only 2-3 hours and are the short alternative to an enduro. Often the C class race is seperate from the rest of the classes and runs on an abbreviated course - typically the race lasts 1-1.5 hours. Check out ECEA, AMA and locally organized races in your area, chances are one of them shortens the race time for the C class riders. In my area (AMA D-7) the AMA and ECEA races are the same time for everyone, but the VCHSS (virginia series) runs the C class before the others on a shortend course.
I don't think you would have a problem with a 2 hour race. Just pace yourself and take a pit stop if needed. No one that I know can ride full out for 2 hours and still be consistent. If you can trail ride for 2 hours you can ride a 2 hour hare scramble race.
I don't know of a shorter type of woods race.
Good luck, race, have fun:)