It sounds like the model is behaving as expected with a variable step ODE solver. Essentially it will take bigger (faster) steps when the data is steady.
When you transition to discrete solver, is it also fixed step? There are 2 potential issues:
1) if fixed step, you must make sure the rate transitions make sense
2) Discrete solvers require discrete blocks such as discrete integrator instead of 1/s
What is the first error you see?
Finally, sometimes your model may be optimized for speed as much as possible and given the complexity of the system it just runs slow. A couple things you can do is utilize parallel computing for multiple runs, use accelerator/rapid accelerator and model references to speed up simulink and finally you can potentially look for places in your model to simplify the system.