I know that SE is thinking of ways to encourage players to use the DF with things like the "MVP Vote" system, so how about this idea:

Grand Company Seal bonuses for repeat dungeon runs if at least 1 party member is a 1st-timer and watched all the cutscenes.

Maybe the speedrunners would be less upset if they got a bonus for being patient and Seals seems a better bonus than EXP (which you don't need at lvl 50) or gil which could be exploited by RMT.

Also to avoid Seal exploitation the bonus would only take effect if 1 PT member is a 1st-timer.