Using a stack for the cleanups reduces the number of nested blocks that
need to be added to properly handle various objects, at the cost of one
block for the stack itself. This lets try blocks be reserved purely for
exception handling.

This fixes a bug where the preprocessing runs would not be cleaned up
if the service timed out while waiting for raws.

The two subsets will now be run separately. There is also an
"afterburner" subset, but it will not be run by Prompt Processing
at all.