Tartan,
Yes, the FTL scheme does account for positioning, at least it does here!! Rest commences on completion of the positioning activity.
As for CAP 371, my Ops controller tell me that this can be superceded by your company's Ops Manual, as does here. We often have crews position home by hire car. However, PRIOR to a flight, our Ops manual stipulates a maximum self position time of 1hrs 30mins is allowable, after which the crew must all be passengers.
Hope this helps
Andy