How about something like…
if (not active of action) then true else if (now - parameter "action issue date" of action as time > 7 * day) then true else if not exists setting "PatchDay" whose (exists value of it as day_of_week) of client then true else ((item 1 of item 1 of (value of setting "PatchDay" of client,("Sunday",0;"Monday",1;"Tuesday",2;"Wednesday",3;"Thursday",4;"Friday",5;"Saturday",6)) whose (item 0 of it as string as lowercase = item 0 of item 1 of it as string as lowercase)) >= (item 1 of item 1 of ((day_of_week of date (local time zone) of now),("Sunday",0;"Monday",1;"Tuesday",2;"Wednesday",3;"Thursday",4;"Friday",5;"Saturday",6)) whose (item 0 of it as string as lowercase = item 0 of item 1 of it as string as lowercase)) )
I think you mostly had the logic you wanted, but I’m not sure “action-start-time” is the right property to check - I’m trying “action issue date of action” instead. You really shouldn’t be hitting a week rollover problem because you’re already trying to handle the 7*day case before it evaluates the day of the week. So I think you’re “action-start-time” logic is always evaluating false.