That’s a nice hike!
I recommend buying one of the new integrated stove-pot systems. They use advanced burners and specially designed pots that funnel energy directly from the burner into the water, not the surrounding air.
JetBoil helped kick start this type of canister-stove design several years ago, and there are now several choices in the category. One is the JetBoil Group Cooking System ($119), which includes a burner unit and a 1.5-liter pot. Alternatively, you can buy the solo-sized Sol Stove ($119), and add the 1.8-liter Sumo Companion Cup. By itself, the Sol has an .8-liter pot, which works for one person but might not be enough for two.
The other choice is the MSR Reactor Stove ($160), which came out about three years ago. I have more experience with the MSR than the JetBoil, and have used it on several multi-day trips. The same principle applies: A highly efficient burner (in this case one that uses both convective and radiant heat) is combined with a 1.7-liter pot that works only with the Reactor burner. The bottom third of the pot has interior channels that circulate heat.
The Reactor is astonishingly fast. You light it, place the pot atop the burner, and within seconds the water is audibly heating up. Boil times are between two and three minutes. I used one on a three-night trip in the Grand Canyon last April, and for morning coffee, instant oatmeal, plus evening soup and meals, we used about two-thirds of an eight-ounce fuel canister. The JetBoil stoves are are roughly as efficient.
Keep in mind that these systems are really best for boiling water—not cooking. The JetBoil line includes a skillet ($45), which somewhat extends its flexibility. But for an out-of-the-box solution for two, I’d go with the Reactor. I’d guess that two eight-ounce canisters will provide enough fuel for your trip, although you might bring a four-ounce canister as backup.