If you guys are all truly sharks, you should be focused on schedule formats that minimize the element of luck.
Ref is right on, an All-Play format is the best for this purpose. But All-Play can also feel a little like the football equivalent of 5x5 roto ... it's not quite as fist-pump exciting when a long TD pass on MNF just moves you from 7th place to 5th on the week vs. winning you a H2H matchup.
So if you want to keep H2H, two "in-between" formats to consider are (1) double-headers (playing 2 teams each week instead of 1, top scoring team gets 2 wins, second-highest gets 1 win and 1 loss, lowest gets 2 losses) ... this works great with 12 teams BTW ... or (2) playing H2H but reserving 2-3 playoff spots for things other than H2H record. So if you have 6 playoff spots, do 3 divisions with 3 champs, 2 next-best All-Play records, and highest remaining point scorer getting in ... if you have 4 (which I prefer), make it 2 divisions and have one All-Play and one point leader playoff spot.
And give out some sort of home-field advantage to the higher-finishing teams in the playoffs ... I like awarding the difference in average weekly scoring for the regular season as a HFA, so if the 3-seed outscored the 6-seed by 65 points during Weeks 1-13, he'd get a 5-point bonus in the first-round playoff game. Sometimes I've gone even higher than this ... that way a dominant regular season means something come playoff time, just as it does in the NFL.