That does help, that's a good bit. But the rolling part of it could be pinching. Can you find a bit like this?
Sorry that's huge
That's a french link, full cheek. Full cheeks are great because they hold the bit in the correct position in the horse's mouth, if you use keepers on them. They also provide a lot of lateral pressure. So when you pull the right rein, it pushes down on the right bar, and pulls the bit slightly through his mouth pushing his left side of his face over. D rings do this too, but not as strongly IMO.
It could also be pinching him where the mouth piece meets the rings, on the corners of his lips (where you say there are cracks). So maybe a D ring would work, but find one without anything pinchy on his cheeks.
When was his last visit to the dentist? Do you know for sure or are you going based on what a previous owner said? I think a dentist may be in order too.
As for the saddle. Just because it fit him once doesn't mean it fits him now - it won't hurt to check. And check his back too.
IME most horses don't gallop blindly off all hot and bothered just because they can, somethings bothering them. It may not be the tack, it could be you (not to be mean) but maybe he's picking up that you're in a mood and getting more bothered by it. Maybe you're body is more tense, which is no good. Maybe you get too heavy with your hands when he gets more forward? Rather than just pulling on his mouth or see-sawing the reins, just do some small figures to calm him down.
This is going to take a lot of investigation and narrowing things down to find exactly what it is that's bothering him, but the bit, the saddle and your own seat and hands are the variable here. I wouldn't lunge him before riding, that'll only get him hotter. If you want to work him before getting on him try long lining him, at a nice easy walk.