Any one of these options works, but a mashup of a few, or all works the best...
1. Freeze cheap beer and load it into your big cooler around a frozen gallon of water or two, then pack full with all your pre-frozen food. Freeze everything. Then top with ice and don't drain the melt. Only beers should be on the bottom layer or two so frozen food wont get wet. Cover with wet towel while on the river, put in shade at camp.
2. Use option one and don't get into that cooler until your cook day and later in the trip (back-up beer), have a second cooler totally dedicated to beer and freeze more cheap beer, put on the bottom and around a frozen gallon of water or two and load really cold, partially frozen good beer on top, cover with ice, shut and cover with wet towel while on the river, put in shade at camp.
3. Have a smaller day cooler in your captains bay and every morning put about 20-40 cool beers in there and stay out of the other coolers, fill with ice the first day and dont ever drain any of the melt until its warmer then the river water then replace with river water.
4. Any beers that couldnt fit in a cooler, but in mesh duffel and put on the bottom of your gear pile in the back or under your table in your front bay's drop bag, they stay out of the sun and are constantly splashed with cool river water in the bottom of your boat. Keep out of sun and every day at camp dump the whole bag (be sure to connect it to your raft) into the river for the evening and throughout the night.
5. Dry ice methods and the option of freezing your whole cooler in a walk in before your trip are great ideas, but one is spendy and the other is tough to pull off unless you know someone with a walk-in cooler and plan to have your cooler there for a few days before you leave. But on a GC trip I could see filling a 150 with only beer, filling the whole thing up with water to the rim and freezing the whole lot and not opening it until week 3, that would rock, but these options are not as easy to pull off at 1-4.
6. The easiest and most likely, drink warm beer... Any beer that sits in the river all night is pretty chilled in the mornings, so just recool every evening/night, make it the last thing you pack in the am, takes up no cooler space and no ice is required.
Oh also, no matter what, its a good idea to have a layer of foam or silver packing bubbles inside every cooler on top, sides too if you're really into it, but at least on top, keeps things a little cooler even when getting into and out your cooler a lot and will sink with your diminishing cooler load as the trip goes on, minimizing the space you want to cool drastically by the end of your trip.
Good thread, the ever important question. I, like you, love to drink beer, so this is important, but when you have to transport over 2K beers for a group of 18 on the middle fork it becomes impossible to keep them all in coolers, and all icy cold, I guarantee no one ever said, nah I won't have your luke cold beer when offered on day 6, 10 or 20 of a rafting trip...
Edit: wow didn't realize I got so carried away there, sorry...