I do those kinds of trips every two weeks of my life.
I am positive it can be done. Its not easy but it can be done. I try and find places like subway for lunch or dinner and eat in my room. I eat veggie subs, or occasionally tuna subs. Mexican or chinese and get rice and beans burritos, or rice and veggies...very filling and tasty to boot, and low calories. I hit grocery store salad bars once or twice a week when i am on the road for dinner...easy to get a large portion of lettuce and spinach with veggies thrown in, or even roast chicken if thats what you want for a bit more protein.
Most every restaurant I have been in will do custom items if you ask. Even when I was completely vegan I was able to make that work on the road.
I stay in hampton inns and have oatmeal with splenda and raisins for breakfast, or I take two slices of wheat toast and make a scrambled egg sandwich with hot sauce. There are always bananas or even yogurt if you want them.
It can get monotonous, and its a bit of peer pressure when you are in a business group, but I have yet to have any negative experiences. Last week I was with a client at lunch, and we went to a diner dive type place. Nothing on the menu was remotely healthy. I finally found what they called a veggie pancake. It was a huge pancake filled with roast veggies (the pancake was flipped in half like an omelet) I just asked for it without cheese, opened it up and ate the veggies...dont think anyone at the table even looked at me funny.