Property tax on Recent Purchased property

[Mak K.]

Hi, I just bought a property in November last year and on my tax appraisal, the property is shown way high. Here are some stats:

Purchase price $225k

Appraised value as of 2018 was $234k

Appraised value as in 2019 is $275k (current)

County- Harris County (Houston TX)

* House was remodeled by the contractor before I bought it. Did not came with appliances. Appliances were excluded from sale.

This is my first time so help me out with my strategy thoughts:

1> Submit Final settlement statement which shows purchase price was 225k. On the settlement, 204k is purchase price and other charges are commission and fees.  Because the sale happened in November, it shows the market value of the house at the end of the year.

2> Submit Inspection report showing repairs. I have a contractor quote of $5k. 

3> Would it make sense to get quotes on AC, Boiler or Roof replacement as they are old? 

So considering points 1 & 2, home value should be $204-$5k = $199k. Is there any hope for point#3 argument?

Do I have a solid case above? Thoughts and Comments please.