In several books on tactics I have read (and I've found it works) in the situation you describe, you are to bear off a bit and aim directly at the skipper of the port tack boat. Hopefully he blinks and tacks early, short of the lay line, at which time you head back up, roll him with the extra speed you gained by cracking off a bit, and cause him two more tacks when he came up short. That's in a perfect world. But lots of things can happen to mess that up!
For instance, if you had yelled "Starboard!!" and he then said "Hold your course!", well, you should already be aiming at him before you yell, because if you change your course after he says "Hold" he could protest you for not holding your course and causing him to tack and/or foul you.
If I see a port tacker coming and it will be close, I either pinch up to make him think there is no way he will cross, and tack early, or bear off and let him cross, if that's what I want him to do. Obviously I want clear air into the mark so whatever I can do to get him out of my way is what I will do.
If I have really overstood by a bunch, I would even come way down, pick up speed and duck him, if it looked like he would be in my way when he tacked. Or yell for him to cross me, as I duck him, but in no case would I allow him to tack in my way. You have to decide which way you want to do it, then yell at him, in case he says "hold your course" back. Of course, if he doesn't say it...
But if he is far ahead of you and tacks on your line into the mark and dumps bad air on you, there isn't much you can do about it unless you get a lift and can pass him to windward. Of course as soon as you round, it's your turn to sit on his air. Payback's a bitch.