Unfortunately UA defies General Relativity, which is why most FE'ers try to avoid the subject altogether. General Relativity states no object may reach the speed of light. No, this does not mean an object can accelerate indefinitely at a constant rate. This means once an object becomes near the speed of light it reaches a sort of universal speed bump. The object can continue to go faster, but only at the expense of serious amounts of energy and at a rate of acceleration that would for experimental purposes be null.
I agree with your position, but disagree with your interpretation of GR...
Imagine that there are two people, one is in rocket and the other is on the ground next to it. They are both initially at rest.
Earth frame of reference:
The rocket launches upward and has a constant thrust (force). As the rocket gets faster and faster, the thrust remains constant but the acceleration of the rocket decreases. As time goes on, the velocity approaches the speed of light asymptotically and likewise the acceleration approaches zero.
Rocket frame of reference:
Because the rocket has a constant thrust, its acceleration is also constant.
http://en.wikipedia.org/wiki/Proper_acceleration#Acceleration_in_.281.2B1.29D