I think it's difficult to fix

  (Edited: )

The only way to ensure that they are not missing clues, is to have a scripted show, where they follow a walk through and merely act surprised as the story progresses. That would be more streamlined, but I think it'd suck the fun out of it for the audience and more importantly for the Seans and Bill.
As you said, those games from a different era were deliberately hard and couldn't be beaten easily, so I don't think it's fair to expect the three of them to do just that. I remember playing the beginning of Indiana Jones back in the day and it took me much longer to figure stuff out, so I don't even see a problem with the pace.
As for the drinks, they seem to kick in by the third segment and even if the pace slows down, the resulting jokes are a massive appeal of the show in my opinion. Take the voice over in the wizard's tower in Quest for Glory part 3 or the "Imagine running laundry driers with this" in a fake German accent in Indiana Jones part 3 for example. Those were hillarious moments and I'm not sure if they would have happened, had they been completely sober.