Thanks for taking the time to post the video, tree was in a tough spot. A few observations that you tell me jump in the river or whatever but I would feel guilty if I saw it and did not tell it.
Free climbing is a no-no, you already know that, takes less that 10 minutes to big shot a line into a tree like that and be secured on the way up.
Helmets and saftey glasses on the ground crew, that black baseball cap is useless if a limb or log falls from any height. Deadwood flying around splatters everywhere, always finds an unprotected eye. I unfortunatly have seen the results of a limb hitting someone without a helmet and I wish it on no one least of all a family member as appears you work with. The guilt and remorse is a life-long thing, think about it.
On several cuts the ground crew was directly under the tree and not looking up or on the way to grab the lowering line. I would not start cutting until all players were in place, especially on dead wood. It is easy to get complacent and assume everyone will be doing what they are supposed to do on the ground, especially if you work with the same people every day. You should still never assume and make efforts to communicate with them before dropping anything, a simple all clear or heads up can safe a life.
While making cuts your rigging line was very close to chain, that is probably how it ended up so beat up. Think about a different rigging setting to keep the rope away.
While dropping logs it looks like there was a chainsaw sitting in the drop zone, second video near the end, those things are expensive, ground crew needs to move them or the climber should look at the scene before making the cut. One bad bounce and the job is free.
You look to be a competent climber and the tree was removed with out incident, sorry if you take this a flame it is not meant as such, simply a call to be careful.