For example,
at first it can be difficult to master button mashing correctly, and not everyone has a sense of rhythm. So I would provide "difficulty modes" with every crafting recipe. Higher difficulties would reward better quality/higher quantity of said item, encouraging perfection.
I would also tie a score with it and a score tracker so players could also have that feeling over reaching a new high score or tracking their improvement over time to see that they are actually getting better.
Higher scores could also also lead to better quality/higher quantity items. In fact, you could make the quality/quantity thing
based solely on score, and difficulty just adds more buttons to press to give the player more opportunities to gain higher scores.
Since it is only a mini game, I would never make a long song for any of this. Maybe 30 seconds at most as we would want to make sure players can get back to what they were doing.
For accessibility (and so players don't feel like they have the potential of wasting their ingredients if they give a poor performance) I think it would be important to offer a "practice mode" or a "high score mode" as well where players can play any of the item songs they want without ingredient requirements so they can learn the songs and hopefully provide a better performance once it comes time to craft the item for real. Allowing players to still set a high score in this mode would also be encouraging to players who just enjoy this game mode and don't want to spend time gathering ingredients just to play this mini game.
(though this will also contradict with the song-skip mode I describe below. You'd need to work out the kinks.)
As for the Atelier problem, I would maybe allow players to skip it either once they have completed the crafting once (this is likely the most accessible for players, but pretty boring) or only allow skipping the song once they have managed to complete a certain difficulty of the song - such as completing the song on hard will allow you to skip the mini-game (I think this one would be more engaging for players since it provides a goal for them to attain.)
You could just give players a "default" quality/quantity of an item if they skip, but I think this actually will be counter productive to the whole purpose of skipping. If the purpose of skipping is to get players back to the part of the game they find the most interesting (exploration/combat/whatever), then only giving players default quality/quantity items is still going to make them feel forced to still engage with the mini-game because the best way to maximize their item production is to play the game properly and not skip it. Basically, skipping becomes a punishment.
Instead, I would opt for providing a quality/quantity based on their most recent high score. This way, if players are satisfied with their current score, they can continue to receive items of that quality/quantity. However, if players wish to improve the quality/quantity of the items they are receiving, they can play the mini-game more in order to improve the item.
