Aha! That seems to be a usable workaround.
I had to suppress the first 'extrude' command that generated the first part that became the array of >1000 parts. It caused a cascade of parts that disappeared due to the inexistence of the first element.
Of course, that has consequences further down the line if there are any elements that depend on the existence of a suppressed element, such as distances, edges as plane references, etc.
The 'suppress' command only seems available on the timeline, and not on the browser. You can not suppress a part, you have to suppress the action that created a part, which ends up suppressing many parts if you are dealing with an array.
It sure would be nice to be able to suppress an entire component, which contains the sketch, the extrude and the elements of the array.
So the practical answer to my original question is that if you have something that is creating many parts and slowing down the computer, suppress that something in the timeline, and turn it on only when needed to create the detailed design.
Thanks! I knew there had to be a way to work with the original file.