This just shows how silly it is to be asking for (and be given) "legal" advice on a car forum. A civil case is not about "guilt"! If it had been taken to court, it would be civil court and the verdict would have been in favor or or against the plaintive. Guilt is not an issue,, liability is!
I still say that the outcome has nothing to do with the facts and little to do with common-sense notions of responsibility. Legal liability will, in the end, depend on which party can make the best impression on the judge (or jury).
If a settlement doesn't work out in a week or so, I would threaten to take him to small claims court and give him a week to pay up. If he doesn't pay up or contact you with a payment plan, take him to small claims court. Let's look at this another way. What if the item that shot out of the mower hit a young child who was lawfully walking on the sidewalk and caused the child to lose an eye. Would everyone still take the "sh*t happens" viewpoint? I think not. It is negligence on the part of the mower man. You have a duty to use the dangerous equipment (the mower) in a manner not to cause harm to another. Harm was caused through his negligence.
After some letters and calls from my insurance (Geico), and me stopping by his house several times, I got a personal check which cleared this past week. What a shame I had to go through this for something he should have just taken care of with no hassles. You simply don't mow with your throw facing towards the street. This was no regular old push mower, it was commercial grade, and his yard is a tangled jungled of a mess. I actually filed a small claims case but canceled it before it went through since I got the check. The guy was pissed that I went through my insurance and he got "threatening" phone calls, but what was I to do when I get no return call for 2 weeks? He claimed that he actually sent me a check a week before, but got returned because of a bad address (what a crock). Also said he had a death in the family and some hardship at work. Boo Hoo. All I needed was a phone call.
Glad you got it cleared up. It's hard to mow always facing away from the street, since normally you mow one way and then the other. But where I live the association contracts out the landscaping, and any time I walk past a mower, they stop mowing until I have gone past. Given what you said about his yard and the mower, he should have done the same for passing cars, or else gone out of his way to always point away from the street, even though it's a nuisance. They don't stop mowing for passing cars here, but they're mowing well-tended lawn, so cars are not in much danger. Pedestrians are another matter, so they stop and wait until you pass, even if the chute is pointed away from the sidewalk!
Next time get a police report at the scene of the accident, 500$ dollars of damage is an accident. Small claims court cost's 100$, without a police report it's a gamble to go to small claims court and you might lose and have to pay court costs, not to mention your time. jmho,ymmv
Due to budget cuts, in my jurisdiction police will no longer come to a scene where all parties are cooperating and there are no injuries. This change in policy only happened a month or two ago, so it's unclear if people will just cooperate at the scene and then be a dick later, like what happened to OP.