It will be interesting to see what they meant when they said they would "work with you". They may not be expecting a $300 bill for the tire.

I would be prepared for a compromise offer. They might also take into account that you didn't see this big pothole before you drove into it. You might be considered to be following too closely if the car in front of you was covering the pothole as you approached, just think if the car in front of you had seen the pothole and stopped suddenly to avoid it, would you have hit him in the rear? That's considered following too closely.
In the state where I work, the property owner is only liable for damages caused by defects on their property if they had prior notice that the pothole was there, and an a reasonable time frame to fix it, and they didn't do so. You said in the draft of your proposed email that they told you they didn't know of this pothole. You also posted that you didn't know the pothole was there before that day. If your state is the same as mine, they could use that argument to deny your payment.
Also, if you are dealing with the company directly, they may have a certain limit they will pay themselves before they kick the claim to their insurer. You might be better off resolving it directly with the company, if possible, even if you have to settle for less than the full $300. JMO.
Good luck.