The problem is more fundamental. If I can't get the simulation to duplicate behavior each time it is run, then things like baking or building a particle cache are kind of "run it and hope it comes out like I want" events -- which is exatly what I've seen.

I was under the impression that baking a simulation is done to save processor time or allow the simulation elements to be adjusted with traditional keyframe animation tools. Similarly, I understood that the purposes behind creating a particle disk cache are to reduce processing time, allow accurate scrubbing in the timeline, and for rendering.

The results from the dynamics system should be exactly the same every single time it is started with identical elements and parameters. Any random elements not purposely introduced by the user should be considered errors and be eliminated.