Well, you answered your own question. Yes, greatly simplify the model and reduce to one part replacing inter-part effects with boundary conditions. You can then build up an assembly piece-wise to ensure it can mesh/solve at each step to increase accuracy and for visualization.
Your static analysis does not appear to be setup to constrain all rigid body movements of your model. This commonly manifests in bodies not having contact sets connecting them to adjacent bodies rather than with fixtures directly. You would want to go through any of the 3 processes here (GoEngineer - Simulation: Diagnosing an Unstable Study) to try to diagnose why your specific study is unstable and then apply contact sets in order to stabilize the setup.