According to the following doc page: https://www.mathworks.com/help/simulink/ug/saving-and-restoring-the-simulation-state-as-the-simstate.html#br_facs Changing the model's configuration parameters will prevent the SimState from being used. Therefore, it seems that changing the sample time between runs while trying to maintain SimState isn't possible unfortunately.
One workaround for this could be to start the simulation at your smallest sample time, and wherever you wish to have a higher sample time, you could set up logic (i.e a MATLAB function block) to only execute certain calculations every x time steps.
For example, if your lowest sample time was Ts1, but the start of your model from t = 0 to n should run at Ts2 (and Ts1 < Ts2), then you could have a MATLAB function block with an "if" statement that only ran calculations every Ts2/Ts1 timesteps for the first n seconds, and then afterwards it would run every Ts1 seconds.
Another, perhaps more straightforward workaround would be to package the higher-sample time section of the simulation into an Atomic Subsystem. The atomic subsystem can have blocks whose sample time is an integer multiple of the outer-model's sample time.
