I think a schedule's a bit inflexible. We all have different priorities in real life and we'd have to coordinate them to find the best schedule. In my opinion, first-come-first-serve in publishing the results (basically, the first person who can be bothered counting up and tallying after all the matches have been completed in a particular match-day) works the best, with at least one other person keeping track to make sure everything is correct. Plus, everyone should (as a matter of sheer care) keep track of their own personal score, just in case the table, after two counts, is still incorrect (which shouldn't happen to often). That's genuinely how it's been done for the past 4 or 5 seasons that this game has been going for and, despite a few minor hiccups which are quickly corrected, I think it's worked fine. There's enough accountability to make sure that no mistakes pervade the table for weeks upon weeks.
Like, most of the time I'm more than happy to do the table if I can be bothered to; but, because we're all in different time-zones, if Nathan, for example, ends up online before me on the Monday/Sunday night/whenever and decides to do the tables, then, well, he can. The vice versa applies as well. The same system works if on a particular Monday, I'm beyond lazy and simply cannot be f*cked doing the tables, then you or Nathan or Joseph or whoever can do the tables. So, really, first-come-first-serve, with people keeping track of their own score to make sure that the person doing the table that week didn't f*ck the count up.