This is a very unfortunate situation and one that I'm glad didn't involve anyone getting hurt.
It happened. How it's dealt with will depend in part on the OP's next move. Nobody on CC has seen the video, but on the basis of the OP's description, these are my thoughts:
1. It sounds as if the corner-cutting by the errant motorist was not posing a threat to anyone (apologies if I'm wrong here). One sees scores of motorists cutting corners every day. Most of the time it is a fairly benign activity, for all that it is lazy.
2. I imagine that either the 'muttering' was louder than intended or it was accompanied by some readable body language. It is hard enough to hear muttered comments from another road user when cycling. In a car, it is almost impossible. My wife often fails to hear me when I'm in the passenger seat... Matthew, are you sure it was just muttered?
3. The driver sounds like a prize turnip and his actions as described sound unmitigably poor and aggressive. Nonetheless, I think the parting comment ("See Ya") must have come across as in some way taking the Mickey or taking a provocative stance. Mad as the driver may be, there are few people who will turn their car round to confront another road user after a mild bit of banter.
I am not in any way excusing the driver. I do not want that sort of person on the road anywhere near my own children (who span the OP's age). Nonetheless, I believe that actions Matthew took may have contributed in some way to turning a poorly cut corner into a face-to-face tiff.
This is not a criticism of Matthew or an exoneration of the driver. It is interesting that you make it clear in the OP that you didn't swear, Matthew. For many people, there is much more to provocation than foul language or physical posture. For all that the driver seems to have been nine parts Loony Tunes, something provoked him.
You mention in the OP that you thought before speaking each time you spoke. It was an ugly situation and you have my sympathy, but perhaps the next time the thought might helpfully be along the lines of "Say nothing".
It sounds like a valuable lesson. You may report this; you may not. Whatever you do, looking at the video again will allow you to see how and why this confrontation developed from what many see as an innocuous and uncommentworthy piece of lazy driving.
Bottom line: I'm glad you're OK.