property tax protest after deadline (Houston, Howe: foreclosure, mortgage, new home)

[moving_houston_soon]

Since I am a new homeowner in Houston, I am still getting my hands around the property tax process. Here's the situation: I just purchased my house for considerably less than HCAD's 2009 appraisal--the purchase price is about 28-30% less than what HCAD says my hosue is worth. Since the previous owners filed a protest with HCAD (and lost), HCAD tells me, by law, I cannot file a protest for the 2009 taxes. However, they have let me know that they think my appraisal is unfair and have been trying to find a way to legally reduce my appraisal. One item they requested was my bank's appraisal for the mortgage process. I will receive this shortly. But should I send it to them? The bank appraisal will estimate that my house is worth almost in between what I paid and what HCAD says. So if I send HCAD the appraisal which lists my house as about 14% less than what HCAD says its worth, but still 14% MORE than what I paid, will I hurt my chances of having my 2010 appraisal set to the price I paid which is much lower than either the bank or HCAD appraisal? Note my home was not a foreclosure.

Thanks!