Quest Kings!

It's always been like that. I think.

It wouldn't let you get a new piece unless you had none in your inventory. So if you had some you had to drop your crack, activate the quest then loot.

I tried dropping it in order to do it again, but it still made me wait 24 hours. Checked it in the data and it also says 24 hour wait.
Just so we're clear, I'm talking about the one before you've defeated Pap for the first time. I was trying to get some spare cracks on my wife-character, but couldn't build up enough extra cracks due to this delay.