Several people have already pointed out the indirect file solution
to Jeff's question.  FWIW, here's what we do (minus some misc.
COMMENTs and TELLOPs).

One reason I jumped in is that have to confess I'm not quite sure
what the difference is in SYSGEN between doing
"MODE=VERBOSE" and not doing it..  but I'll bet somebody on
this list knows....  Whatever the precise difference, it's my
understanding that the VERBOSE option stores more "stuff".
Since we want everything to go to tape, we've always done the
VERBOSE thing.  We also save the date/time of last successful
SLT + STORE to a file in our SYSOPER group....

If there is a way to do what Mike Hornsby mentioned;  i.e.:  Include
the list of files STOREd at the end of same tape they are STOREd
too;  I would be interested in finding out what it is.  Our job saves
the *previous* list while it's doing the current STORE;  but since
the file being written to by the current evolution is of course open
for writing we don't get that one....

Anyway, our Job does:

!JOB JBSLTFU7,MANAGER.SYS,SYSOPER; HIPRI; OUTCLASS=124,1; PRI=CS
!COPY ALLFILES,ALLFILBU
!CONTINUE
!PURGE  ALLFILES.SYSOPER
!BUILD    ALLFILES.SYSOPER; REC=-132,,F,ASCII; DISC=100000
!FILE   SYSLIST=ALLFILES.SYSOPER; DEV=DISC
!FILE   T; DEV=7
!FILE   SYSGTAPE; DEV=7
!SYSGEN
TAPE MODE=VERBOSE STORE=!SLTFULLL
EXIT
!RESET SYSLIST
!CONTINUE
!PURGE  SLTDATEF.SYSOPER
!ECHO   SLT Created on !HPDATEF at !HPTIMEF > SLTDATEF.SYSOPER
!SAVE   SLTDATEF.SYSOPER
!EOJ

And our indirect file (minus some misc. minuses):

/SYS/ , / - /SYS/ - /TEST/ ; DIRECTORY; ONVS=
MPEXL_SYSTEM_VOLUME_SET,USER; SHOW

This gets DIRECTORY for both the <long name> and USER
volume sets....

Ken Sletten