Confirmed my noise is coming from the tips vibrating on cold start. Pulled them off and noise was gone. Here is the video:
Put them back on, pushed all the way in, and secured tightly. Same vibration noise was back, and you can clearly see the tips vibrating, causing the noise. Here is that video:
Seems to simply be a consequence of poor design, and I'm wondering if the new style carbon fiber tips with the clamps will fix this. If not, I'll probably go with the chrome tips. This noise is too annoying to tolerate on every start up.