We did the Trek in February, and I took my Nikon D5000 with an 18-250mm lens on it. I used my regular camera neck strap and felt secure with my camera. I wouldn't feel comfortable changing lenses or bringing a second lens on the Trek. The multi-pocket vest probably won't help you, because their vest is the outer layer - the safety harness clips are on the vest, and there's no way to wear a jacket or vest of your own outside it. Since their vest is securely fastened all over any vest or jacket you're wearing, you won't have access to your own pockets and their vest has fairly small pockets. Small point and shoot cameras will fit, but a DSLR lens probably would not.
Unfortunately, on our tour it rained fairly hard much of the time we were on the walking portion. I didn't realize that my raincoat would be completely covered by their vest, so I wasn't able to protect my camera with my raincoat at all. One man on our tour brought two DSLRs (yes, TWO) so he could use two different lenses the whole time. He brought plastic bags to cover each camera, and they allowed him to bring the bags attached to his vest (to make sure they didn't end up at the bottom of an animal area). I was lucky that my camera dried off and suffered no damage from the rain, but if I get to go on the Trek again, I will definitely be bringing a bag to cover my camera in the event of any rain in the forecast.