Leaving out Boeing would be budget suicide for NASA.
No one should be left out because there should be no contract. Instead, NASA should be fostering a spot market for launches. They should have a separate bid for each launch: "We want X satellite in Y orbit, and insured for Z dollars." Then give the launch to the lowest bidder. That way each company can work continuously to cut costs and improve services, knowing that if they leapfrog the competition, they can win the next launch, instead of being locked out for years.
That is not feesable. It take years to be trained to fly in a spaceship - whether the lifting body like the Shuttle or Dream Chaser, or a capsule such as Soyuz, CST-100, or Dragon V2. You have to build not only the rocket, but a tower to carry the crew to the top of the rocket along with an arm to get the astronauts into the vehicle (which is not compatible/spacecraft). Escape systems need to be installed. It's very expensive, and it would never be built without assurance that the demand is there. At this time, there is no market for launches except from NASA or ESA. Cosmonauts would ride Russian spacecraft, Indians and Chinese are developing their own systems, etc. The public demand is too little at this time. Without a long-term contract, NASA is not enough for your proposal.