Pretty much all of the HOAs that are de facto zoning boards of the Houston area would most definitely prevent you from doing anything like that. HOA by-laws are where you'll find the real zoning regulations over there.
I wonder how well those hold up in court if you really wanted to build. I could imagine a Texas court being friendlier to development.
You mean trying to violate the deed restriction with compliance mandated by Section 26-475 (and other applicable places) of the Houston Code of Ordinances? I don't think a lawsuit would hold up very well, unless you could could convince the judge that the city can't regulate land use.