Make story mode dungeons reward tokens
I agree with you that finding party members for a dungeon in Story mode is a really difficult task and there are very few players who are seeking to do Story mode. Even fewer players who have done the story already are willing to help. Personally, it took me days to find a party for HotW and CoF.
I agree that giving a fraction of the tokens that would otherwise be obtainable in Explorable mode would provide more incentives for veteran players to join on Story mode. A fraction is given simply because the Story mode is typically easier than Explorable mode, to prevent possible exploitation.
Alternatively, we can have people obtain 20 tokens per dungeon’s Story mode (replayed) per day, this would encourage veteran players to assist other players in their Story mode. I would also need to state that a Story mode completion should not exhaust the 60 tokens you get when you complete a dungeon on Explorable mode the first time in that day. It should be an independent condition and reward.
Another possible solution is the choice (of the player who initiates the dungeon) to upscale a Story mode’s difficulty to that of an Explorable mode’s difficulty, this would justify handing out tokens to players who have already completed the dungeon. The choice of whether or not to give tokens to the first timer does not really matter, you can argue either way.
TL;DR It’s tough finding a party for Story mode, because most players are unwilling to do Story mode more than once. Therefore, there should be tangible incentives for these players to assist others in Story mode.