Really, the cooler size you need depends on what kind of food you bring. We like to have as much fresh or frozen meals as we can. We also like cold beer, but it's not like your going to fill the damn thing with beer. Well, some might.
We've only been doing mutliday trips for 9 years, but our go to cooler for most trips, be it a weekend or 8 day trip is a cheap 120 qt igloo cooler. We've modified it a a little with 1'' ethafoam glued to the top and foil bubble wrap lining the inside. We've compartmentalized it with foam board to turn a 1/3 of it into a freezer section that we put dry ice in. For us, 120 qt. seems just about right for anything short of the GC. For the GC we bought a 150 Igloo Yukon cooler and it's killer, but it's big and heavy. I'd take it on the Main though. August on the Main...you can't have too much ice for your beers.
Be careful with Yeti and Engel "sizes". If you use their interior measurements, the Yeti 160 is only 135 qt. and the 125 is only 107 qt. Engel isn't any better.
BTW, Doing the math on the Blackrock coolers, they seem to be true to size. Sale going on now. I have to admit, I'm eyeing the 110 qt.
FWIW, 57.4 CI = 1 qt.