“Cross Hashed Lines Separating Hov Lanes”

The signs along HOV lanes admonish us not to enter or exit these lanes except at marked points. Assuming that there are flashing lights on a vehicle stopped on the left side of the highway, is it lawful to ignore these signs in order to obey this [move, where possible] section of the act? (By the way, is it normally an actual offense to ignore these signs? What is the penalty?)

To the best of my knowledge, yes and yes (though I don't have personal experience with HOV lanes).

Section 154.1 (3) of the HTA seems to be a catchall category covering all HOV offences. I believe it's what you'd be charged under if you crossed the striped line. It carries the usual $110 fine and 3 demerit points.

The actual HOV rules themselves are found under Regulation 620/05 of the HTA. Section 3 of the regulation states "no person shall operate a motor vehicle or commercial motor vehicle to enter or exit a high occupancy vehicle lane by crossing a buffer zone", but goes on to list several exemptions.

Most of the exemptions are for emergency vehicles, but two apply to regular motorists. The two times you're allowed to cross the striped line is when directed to do so by a police officer or when complying with the requirements of section 159 (the "move over" law section).