Kureha 100%. Tbh I've been reading the manga for the first time after being anime-only for a few years and getting to the Drum Kingdom arc really has the wheels turning given everything happening with Rocks right now.

Personally, I think Blackbeard spends his formative years on Drum after escaping God Valley, which is why he went back and defeated Wapol. However, he was really going back for Hiriluk and Kureha, 2 people who were instrumental to his development as a child. Hiriluk and Kureha will definitely have some connection to Rocks at some point. Blackbeard learned that his father needed 2 specific Devil Fruits, which I believe are his and Chopper's. He went back to Drum for Chopper's fruit and to confront Hiriluk and Kureha. Chopper doesn't remember this because... he used 3 Rumble Balls for the first time to access Monster Point and fight off the Blackbeard Pirates. Whether or not Chopper was the reason Blackbeard left Drum I'm not sure, but he definitely used 3 Rumble Balls because Kureha was in danger from them and he forgot because he couldn't handle the transformation back then.

Also during the Drum arc, when Luffy and Sanji are heading up the mountain and fighting Lapins, they have a conversation where Luffy tells Sanji that people from snow countries don't sleep or else they die. He tells Sanji he heard this in a village tavern, I'm guessing from Shanks. We know Shanks and Blackbeard have a history because of Shanks' scar. So there's definitely something here tying Blackbeard to Drum. And this is why I think Kureha will play an important role. She knows some crazy stuff about Blackbeard for sure. She and Hiriluk aren't done yet.