The "penalty" you get when missing or declining a queue is virtually nothing, unless you do it repeatedly. You get like 3 and then you get a 30-minute debuff where you cannot queue up. When the day resets, your penalty count resets.

So, you can miss one or two queues without worry. This should take care of the rare instances where the queue pops but you cannot access it (to be fair, during most cutscenes you do have access to the UI). Even if you do miss a third, which would be very, very rare, you only need to wait thirty minutes before trying again.

If you are missing three or more queue pops in a row due to cutscenes, I dunno what to say. I've personally missed one here and there, never missed two, never even came close to missing three in a 24-hour period. Maybe try some crafting or inventory organizing or Gold Saucer while you're waiting in the queue?