Yeah it's way late to mention this now but, still no rework for this, Square...?

[Anapingofness]

The problem is that if they're run at their normal pace with cutscenes intact, those dungeons take 45 minutes to an hour each. When even the more challenging dungeons can be completed in 20-30 minutes, asking people to wait so you can watch something (that you can just watch again later in the inn) is rather absurd.

Absurd? Hardly.
Furthermore so what if they take 45min-1hr to do? Those dungeons are under a very specific category so if you queue up for the Main Scenario anything the expectation should be that you will run into newbies who want to experience the storyline and the cutscenes- NOT the opposite.
Nobody put a gun to their heads and told them to queue up for those fights. There are MUCH faster ways of getting Poetics than going into those fights, there have been for a while now.

OP, I will not tell you to resort to YouTube or the Inn to watch your cs. I recommend that you go in as an undersized party. You don't even need a full 7 people, you can get away with 2-3 people easily. It may even make the dungeon a lot more fun for you. In fact, when my sister's alt got to CM and Prae we duoed it. Granted, I was stupidly over geared- and to be honest with you it was a lot of fun.
On the bright side, you won't have this problem after CM and Prae.

Again OP, I'm sorry you had such a frustrating experience.
The people who rushed ahead were jerks and they really had no business queuing for Main Scenario roulette if they weren't going to accommodate players who want to experience the story.
However, don't let a few bad apples spoil the bunch. The main storyline gets pretty epic and it sounds like you guys were enjoying yourselves up till other people decided to be unkind.