Standard AR parts require a 10.5" barrel to make 29".
You may have to get them info on how you were going to do it with a 9.75" barrel.
That was my thought also. You typically can't get >29" without going to some lengths (see what I did there? ) on the stock. Any chance OP had a math error and the ATF noticed that?
Also for the OP, yes, suppressors are generally considered flash suppressors under the law.