"New Venture gear is co-owned by Chrysler and GM. Or was at one time. "
Correct. The company's name was New Process Gear (owned by DC) until the "New Venture" started with GM. The relationship with GM dissolved a year or so ago. The worry around Syracuse, where one of the NVG plants employees nearly 4000 people, is that the company will be sold. The other plant in in Muncie, Indiana.
I believe the Syracuse plant primarily makes transfer cases (for GM, DC, and others) and they used to make the 5 speed manuals for DC small vehicle line (shadows, sundances). I don't know if they make transmission for the Neon/PT cruiser.