Guilt was admitted, I followed their instructions, and now I'm out $800+?
Why does the cause of the road damage matter? The road was damaged, and it was repaired immedietly. - Also admission of guilt. So who is liable in this situation?
First of all, any "admission of guilt" is just your perception and is in error.
In order for any person or entitly to be liable for your damage, your damage must have been caused by negligence.
An acknowledgment and repair of a hazardous condition is NEVER an admission of liability. And telling you where and how to file a claim is also NEVER an admission of liability.
Whether there was negligence depends on factors not yet revealed.
Like when and how did the condition occur, when did the DOT have notice of the condition, and when did the repair crew get sent out? Answer all that and I'll give you my opinion as to whether the DOT was negligent.
As for who you sue, it's never the insurance company, and not likely the contractor either since the contractor was acting as agent for the DOT. That leaves the DOT, which you can, indeed, sue under your state's tort claims statutes but you have a limited amount of time to do that. And there's no way to predict whether you win or not.