I love that cooler. Did it take a crane to pick it up when it was full of buffalo?
We killed 2 average sized elk in NM and fit them just about all in 152 quart igloo coolers this fall. If you didn't bone out the fronts, there was no room for ice they just barely fit. To be safe I think I would say, (and what we will do next time) that you can fit all 4 boned quarters with room for ice in a 150 quart cooler. You then need a smaller secondary cooler (50 quart) for the backstraps/tenderloins/neck meat. And I'd take a separate smaller cooler to keep the cape in, you want to keep that cold and dry, so may want to pack with ice on bottom and something in there to keep the cape out of the water and drain often.
If there is 2 of you, you can combine, so 3 150 quart coolers will contain all the elk meat off 2 bulls and 1 more 100 quart for 2 capes and yellowbellies (coors original).