People from SHA will read this site ..... just depends on if they read this site for other reasons of course. They aren't seeking out threads mentioning them. But to that, I don't think the OP fully expected an SHA audience and was posting more or less to vent with tongue in cheek.
Chips/dings from construction projects are a gray area altogether. On SHA contracts, you are to housekeep your work area. The definition of this is limited and is applied against nearly all their contracts regardless of scope (overpasses vs. repave, etc. which carry far different operations). For road rebuilding, there is typically a brush sweeper immediately following the mill machine. This tends to clear up a lot of the millings. Even with the best efforts, some pebbles do escape and more develop as the narrow ridges between the grooves can crumble and create new "pebbles." There simply isn't a foolproof method other than constant sweeping.
When it comes to recovery of costs for damage, you likely won't get anywhere unless you catch someone on a very nice day. If you contact SHA, you will get passed around to a head department, down to a District office, to a contract team to a project engineer. If you're lucky, they may try to push your bill to the contractor who will simply rebut it saying they've met their obligation to the contract in terms of protection of the public (warnings, MOT, site cleanup, etc.) and that any sustained damage would then go back to SHA. More so, there is virtually no way to actually PROVE the damage was done on their site other than you saying so. Contractors have risk management teams who deal with this all the time.
Basically, if SHA expected to eliminate ALL potential damage, they would require contractors to do more .......... or to close the roads while the operation was taking place. All of which would cost them significantly more money.
You may ultimately get your $20 ding repair but you will spend 100x's that in your time trying to find someone willing to pay the bill.
