Will sleeper-berth periods that are a minimum of 7 hours in duration extend the 14-hour limit, if at the end of 11 hours of driving, the driver takes 10 consecutive hours off-duty?

Yes. The federal hours-of-service rules for drivers of property-carrying vehicles state that any sleeper-berth period of at least 7 consecutive hours will be excluded from the 14-hour calculation as long as the driver also gets a separate rest break (either off duty or in a sleeper berth) of at least 2 hours, with the two breaks adding up to at least 10 hours. Getting a 10-hour break serves as a break of “at least” 2 hours, so it can serve as one of the two qualifying rest breaks needed for the split-sleeper option. See 395.1(g)(1)(i).