Quote Originally Posted by RossWaddell View Post
Here's a video which shows how the two LEDs start off in sync (first 10s) and then gradually go out of sync
It should be easy to prove to yourself it has nothing to do with the transistor - make the second circuit exactly like the first and observe how EXACTLY the same loss of sync happens.
Having 2 unrelated free running oscillators stay in sync is not a reasonable expectation. (Oscillators 101)