The more I ride the bike the better I understand the problem. It's not that I'm reaching too far forward, indeed, a longer stem would be even more comfy. And that means, as you've said above, that it's my body that's actually tilted forward, which distributes weight differently. Bringing the bars back towards me will likely make me feel cramped, it's the seat that has to go backward, but that's already as far back as it can go. So it's basically just getting used to the new geo and aiming for trails that have more ups and downs than flats!