It was probably cheaper, but the main reason is that GDLS and GM were competing for the Stryker contract together, and since LAV III is a GDLS product, they just put a different turret on it like you said, changed a few other things and submitted their proposal.
I don’t think they got hulls from existing production line either, we ordered thousands, on top of domestic and other foreign orders for LAV 3, they probably had to open a new one