Federal - OAL > 26", less than 16" rifled barrel, no stock, pistol grip + vertical foregrip is a non-NFA "firearm" as you say. That said, the thing which keeps it out of AOW land is the notion that OAL > 26" is a presumption that it can't be "concealed on the person," and that presumption can be rebutted if it actually is concealed on the person. You can read all the ATF opinions about Shockwave-style firearms for the legal logic there. I personally find that it might well not hold up, but, my goal is also not to have to go to court to prove it. The phrasing for AOW is concealed on the person though, so federally it doesn't matter if it's concealed or not as long as it's not on your person. Back seat under a blanket or in a case would be kosher for federal laws, in general.
State - We bandy about terms like "long gun" a bunch, but the main concern for carrying something in Texas is whether or not it is a handgun as Texas defines it. Texas says ""Handgun" means any firearm that is designed, made, or adapted to be fired with one hand." Something with a pistol grip and a vertical foregrip pretty plainly isn't "designed, made, or adapted to be fired with one hand" I would say. The reverse of this is worth pointing out, namely the case Ford v. State, 868 S.W.2d 875... Ford was caught carrying a double barreled shotgun which had been cut down to look like this:
The court convicted him and upheld appeals for it being an illegal SBS but also said that it was a handgun under Texas laws as well because it had been adapted to be fired with one hand. That appellate opinion would be pretty strong precedent that something built to specifically use two hands, like a VFG, would not be a "handgun" as far as Texas goes no matter how big or small. If it's not a "handgun" then LTC and concealed/open with MPA doesn't matter, just general firearm restrictions for state laws, and the fact that it's not a "rifle" or "shotgun" isn't really a state factor.
Take it all with a grain of salt. I think I'm right because I can read words written into law, but it's a thinner line than I would like it to be too often. Being totally safe is why I like to buy me some stamps on a Form 1... money well spent.