I stumbled on these two videos and I think I will follow his recommendations to try to reduce my runout.
TTS Runout - R8 Collet - YouTube
TTS Runout - Holder - YouTube
I also plan to take it a step further and add a chamfer to the bottom 3.5 mm of the collet. I'll do this because I noticed a little gouge on the inside of my TTS collet created by the relief edge near the bottom of the shank of TTS tool holders. I believe the gouge is increasing the runout of the tool holders.* A chamfer there will also make inserting tool holders easier. Lastly, since TTS tool holders have the relief on the bottom of the shank the collet isn't clamping in this area anyway.
* I actually just finished boring out the first 3 mm of the inside of my TTS collet. I tested the taper of a single TTS tool holder before and after the bore. Before it had a consistent TIR of 8 tenths and after it was 3 or less.