I could be wrong, but I don't think your plan will work. Unless they've changed the rules since 2015, I don't think you're allowed to camp in the Beaver Falls area. Even though campsites aren't assigned, I'm pretty sure you're only allowed to camp in the campground area, which is between Havasu Falls and Mooney Falls. Plus, I would NOT be comfortable going down Mooney with a heavy backpack on. I think that could be dangerous. When we went down Mooney, we only had small daypacks.
For our trip, we went down to our campsite the first day, set up tents, rested, and explored that area. The second day, we explored further downstream, going down Mooney and to Beaver. Then the third day, since we knew what to expect, we got an early start (6:30 am) and quickly made our way down Mooney, past Beaver, and then past the boundary between the tribal area and the national park, and made our way to the Colorado. We had a firm, turn-around-no-matter-what time of 12:00 noon, since we did not want to go up Mooney in the dark. We got to the Colorado around 11, spent an hour relaxing, then headed back up and got back to camp around 5:00-5:30. Sunset will be around 6:00 pm for you in February; for us in June it was much later. Maybe you'll be faster at figuring out the route than we were and won't take as long as we did. Also, it was hot, so we did relax in the water a bit in the afternoon on the way back up and probably could have made it back up to camp more quickly than we did if we had needed to.