It is illegal, with limited exceptions, to knowingly possess a machine gun, short-barreled rifle, short-barreled shotgun, silenced firearm, or any part or combination of parts designed or intended to be used to convert any device into a prohibited firearm.
A state cannot declare illegal that shich the Feds have specifically declared legal. A properly papered SBR is specifically legal under Federal law. Texas has similar wording in our laws but it is still legal to own, sell, manufacture, possess, etc a NFA firearm in Texas if it is done in accordance with Federal law.
Check with your chief LE officer (Sheriff/Chief of Police) to see if he/she will sign off on the paperwork. That is the stumbling block. If you cannot get the application for the tax stamp signed off, you have a much harder time getting the weapon approved. Some espouse the virtues of doing the paperwork under a trust, but I am not very familiar with this tactic.