Hello. Problem seems to be related to the time step. Although the normal mode integrator allows running MD roughly with the same time step as a classical MD trajectory, you can encounter resonance problems (given that this is a form of multiple time step integrator), particularly with large bead numbers.
I tried running your examples with a time step of 0.5fs and there is no divergence or instability. You could probably also stabilize simulations at 1fs by tuning the thermostat, using a BAOAB integrator, or the Cayley integrator (which is not super-well tested, but is meant to address exactly this kind of problems).
Hope this helps. At worst, you can prob get away with 0.7fs which is not that much slower than what you were using.
MC.