Mitch,
It is difficult to understand your mechanism without seeing a model of it. Are you running a dynamic or kinematic analysis? What kind of joints connect the cylinders? I'm confident we could get your system running, but I'd need to see the mechanism to lend a hand. I've successfully run quite a number of ICE, valve train systems and hydraulic actuators in MDO, many of which were highly non-linear as well, so I'm sure your problem can be solved.
Chris