The selection of "Static, general" or "Dynamic, explicit" really has nothing to do with if the material model is time-dependent or not. I typically recommend implicit simulations (static, general) for all cases unless one of the following conditions apply: (1) the applied loading is so fast that inertial effects become important; (2) the simulation has large sliding contact or some other feature that make it difficult to make the simulation work using an implicit approach.
In your case you should be able to extract the time history results without too much problem. All you need to do is to specify that ABAQUS saves the desired data with a given frequency. That frequency has nothing to do with the number of data points in the load amplitude definition.
Jorgen Bergstrom, Ph.D.