Are there locations/altitudes with minimum speed requirements?
The way it works is you file your flight plan for the NAT with a proposed Mach #, but when you get your Oceanic Clearance they will assign Mach #s for each segment of the NAT and that's what you have to fly unless cleared for a different speed.  The adherence to assigned Mach #s are the only assurance of separation once out of radar coverage.

Perusing the NAT Operations Manual I couldn't find anything that gives a minimum Mach #, but if you were unable or didn't want to maintain the Mach # assigned, you would probably be given the option of flying down below RVSM airspace, or taking an off-NAT routing like the northerly "Blue Spruce" route (which airplanes use when they have to stop in Iceland for fuel because they don't have the range for the NATs).