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I've played the game once already. I've uninstalled completely and reinstalled three times, and still every time I try to start a new game it starts with the last save from the first game. Anyone else run into this problem?
Yes! I got to the final area before I technically was supposed to -- there were still areas to visit, etc. So maybe I 'broke' play?

Anyway--that game ended and I was excited to start game+ -- look for new things and for sure not end the game early!

But just like you, game starts on the last chapter of my original playthough. I eventually got frustrated and deleted the original game. Probably should have reached out here first--that was many hours of effort tossed out.

Hope there's and answer to this. I've been too worried it'll happen again to start another (technically brand new) playthrough.
It's been a while since I played, let alone started a new game(+), but are you sure it really is the last save? If I remember correctly, the game starts with its "last" scene, near the top of the mountain, which means every new game+ should start there, as well. (The whole game is a sort of flashback from that moment, I believe.) Just keep playing and see what happens?