Does the theatre require that you hand out clean and updated running sheets to the crew at each rehearsal? Many of the stagehands I've worked with get very attached to their highlighting and handwritten notes, and I can't pry the old sheets out of their hands until we actually stop making changes. They don't want new sheets each day--that just means they have to mark them up all over again.
This gives the ASM a touch of flexibility. You get the information from the crew, either in a meeting following the rehearsal, or actually during the rehearsal if there is time to talk. The other way is to collect the sheets, photocopy them, give each person back their own sheets and do the clean update without such time pressure. (As the ASM, of course, whether there are updated sheets or not, you must have notated each crew member's current track for your own reference.)
If you must update, publish, and distribute at the next call, and you really have 2 hours of work, do an hour after rehearsal and an hour prior to the next call. 'Cause if that's theatre policy (and I just can't quite picture that,) that's why we AEA SM's get paid the bump-up in a LORT Tech. Week! No counting SM hours in Tech Week. (No comfort there, just the facts.) Or perhaps you can split the job to update SR and SL on alternating days or split the work with a knowledgeable PA. Creative solutions like that can help too.
I'd like to know more about your theatre's policies or "traditions." Sometimes they are worth changing!
Good Luck,
RuthNY