Finally! I can contribute to this thread instead of just feed off y'all's hard work and research!
I'm actually a property tax consultant! I focus on commercial but have experience with residential. Have y'all heard of binding arbitration? Some of this advice is county specific but in most of DFW, for example, I'd recommend what's called a "topline" or "joint motion" on whatever offer the district gives you when you file protest. After that, file binding arbitration. It costs around $500 but you tend to get a way better settlement than most people would achieve at a normal board hearing. If it looks like it's going nowhere or if you find out you really don't have a good case, withdraw your arbitration in your 45-day settlement period and get your $500 back. If you get an offer your like, in the settlement period, accept it, withdraw your arbitration and get your $500 back. If you think you have a good case and you still don't get a good offer, take it to the arbiter. If they rule closer to your number than the disctrict's number, you get your $500 back less $50.
Edit: I'm seeing a lot of focus on market value in this discussion. I'd encourage everyone to read the taxpayer remedy in the tax code regarding equal and uniform! Basically you need to be assessed equally to your neighbor regardless of the fair market value of your home. The code is intentionally vague and allows you to select a "reasonable number of comparable properties, appropriately adjusted". And this isn't related to what they would sell for, it's related to how and what they are assessed at on a per SF basis. You can see how there would be some good room to work with there.