Well, that was weird. As I said, I left the writings behind and when I arrived in China, I got a message that basically told me off for losing them.
At the end of the vacation, I received the usual message telling me that I had twelve hours left before I had to go home. Then I got an opportunity message congratulating me for finding the writings, and my Sim had the little 'deliver the writings' direction appear on his bar. I checked his inventory, and the writings had rematerialised. I promptly delivered them, and was given my reward.
When I got home, I looked in the chest. The writings were still there. Same writings. My Sim wasn't even in any tombs when the duplicate writings appeared in his inventory--he'd been doing a different adventure since then, and both of them were for the special merchant in China. She was supposed to be taking his platinum and lapis lazuli to make a statue, and I forgot to check if that adventure was still active or whether it's been lost now.
So, I'm not really sure what happened, but it appears the game does try to make sure you can complete these things! I should probably go back to China and see if I can resume my statue quest, but I'm itching to explore France or Egypt instead.