I was able to get my T-Rex swallowing the ball 100% of the time and thought I would post what I did in case others have the problem.
When I added the improved T-Rex body my T-Rex would not stay vertical. My mechanism had some slack in it and as best as I can tell, the added weight of the new body was enough to make the T-Rex lean forward a little. I tried a new up/down motor to try and get rid of the slack as its gears seemed a little sloppy. This did not fix the slack issue. Next, I shortened the link arm from the motor cam to the bottom of the T-Rex frame. I did this by making the angles more acute where the link arm has a short horizontal offset bend. By bending the horizontal piece to be more of a "Z" shape I was able to take about 1/8" out of the link arm length and now my T-Rex is vertical with no slack (you cannot push the T-Rex forward or backward a little, like before) when the motor is all the way up. This seemed to help the ball swallowing problem a little. That is, about 50% of the time the T-Rex would swallow the ball when it chomped (but not immediately upon the T-Rex becoming vertical).
My T-Rex's jaw was open enough when the T-Rex was vertical that the ball could fall out the mouth. I added a felt pad to the pad under the chomping solenoid as suggested by Winteriscoming. This kept the ball from falling out, but originally I had such a thick felt pad (I am using one of those stick on pads that Home Depot sells for sticking on chair legs for sliders) that the jaw was completely shut when the T-Rex was vertical (i.e., the jaw did not move when he chomped). Still, the ball did not roll down his throat and now without the chomping, there was nothing to cause the ball to roll back into the throat. I used an Xacto knife to make the felt pad thinner (down to about 1/8") so the T-Rex chomps when vertical, but still not swallowing the ball 100%.
I noticed that there was some slack in the chomping mechanism. That is, I could push the chomping solenoid in by hand and the jaw could still open and close a little. When I originally installed the improved T-Rex I didn't want to drill out the rivet in the jaw, so I ordered a new one from Marco. The jaw link arm from the chomping solenoid to the jaw was difficult to get into the hole on the jaw, so I drilled out the hole on the jaw a little. It turns out that this made the hole large enough that the link arm could move up and down some without engaging the jaw. I ordered another jaw from Marco and while I was at it I ordered a new jaw link arm. It turns out that my link arm was slightly shorter than the new one from Marco (I think Winteriscoming mentioned that there were a number of the link arms that had issues and you should check them, but mine appeared okay when I looked at it with nothing to compare it to). The combination of the longer link arm and the jaw with the original/smaller hole tightened up the slack in the chomping movement.
With all of the above, my T-Rex is now working 100% with the improved T-Rex. Sorry for the long post, but I wanted to post my experience in case it can help someone else with T-Rex problems.
Ross