You are absolute correct that it will affect the gait and we actually did a short study on the effect of back flexion on running speed and produced an abstract for SVP in 2007: “What if” Testing in dinosaur functional anatomy using evolutionary robotics. Sellers, W. I. and Manning, P. L. In: Society of Vertebrate Paleontology Annual Meeting; Austin, Texas, USA. Journal of Vertebrate Paleontology V.27(3): Society of Vertebrate Paleontology ; 2007. p. 144-144. We never did anything more with this but this is certainly an opportunity for someone! My feeling is that it whilst it could make the dinosaur faster, it probably won't reduce the load on the legs and that's what's limiting the speed.
If the tail and torso of the Tyrannosaur were to move up and down during locomotion at just the right rhythm maybe a decent amount of the dinosaur's mass could have momentum timed to oppose and lessen the impact transients at each footstep?
This would be related to (and require) back flexion, but would really about smoothing out the impact of some of that body weight over a longer and later portion of the step rather than having it all hit more-or-less at once.
Just an idea.- Zach Fine •