Wow! Amazing responses, great suggestions! I stepped away and watched the game last night. Took time to digest answers + I wanted to try the suggestions before responding. I have solved the problem.
Causes:
1) Pilot Error. Study Rest was not concentric with the chuck.
2) Too fast RPM
3) Chuck Jaws Too Slick
Details:
1) I rarely use the study rest & forgot/bypassed the setup process. The last time I used this rest, the diameter of the workpiece was (sort of) the same diameter. Delrin size was 2” x 12” round. I placed the material in the chuck, installed the study rest about 3” from the end, wrongly assuming the bottom two roller guides were concentric with the chuck. Touched the Delrin with the top guide & dial indicated from there. Of course, I got a good reading & believed everything was good to go. The whip (Which I could not see with the eye) helped cause the material to work its way out of the chuck.
2) RPM was at 1250.
3) Although I have never had any issues with ferrous material, the jaws are apparently too slick.
Solution:
1) Used correct setup procedure. With such a long piece of Delrin I used the bottom of the study rest to support the very end of the material, while I dial indicated the runout near the chuck. Adjusting the 2 bottom guides during measurement until the indicator near the chuck read true. Then carefully moved the study rest as close to the chuck as possible & readjusted the 3 roller guides to just touching the Delrin. Moved the study rest to about 3” from the end of the Delrin & secured.
2) Reduced RPM to under 500
3) Wrapped 150 grit sheet rock screen between jaws and Delrin.
Doing the above resulted in the stock staying in place while spinning (No live center). Using a live center along with the study rest during turning & facing operations functioned fine.
I still feel like this 3-jaw does not hold the Delrin well enough. I believe I will in the future make a split sleeve to place under the jaws.
Again thanks to everyone for their help!