Does anyone have a report that will parse something like
'q act' and generate a report on backup start, backup stop,
files inspected, files expired, etc.?

I would suggest looking at the q act command.  If you add the option
originator=client and filter on msgno, you can get pretty much all of the
information that you need.  You may need to do some math with timestamps
and elapsed time, but the information is there.  You might also want to
look at using the accounting records produced by TSM

Alternately, TSM Operational Reporting would also be an option.

Ted