Yes, you could do that. But then you'd still be out the money needed to buy the new barrel/upper and new buttstock. And you'd have an unused short barrel on your hands that this same bureaucrat might decide to declare an NFA item.
That's the problem when these things are defined by "rules" rather than "laws". While laws can be changed, rules can be changed more frequently and more easily, and rules are also more subject to modification with the changing political winds after an election. A great example of this is Obama's DACA executive order (same as a "rule" basically). Now Trump could change that in a heartbeat if he wanted to. I highly doubt he would, but the point is that he could. And if he did, that would throw a wrench into many peoples dreams. Just like a rule change regarding AR pistols would.
Not that "laws" aren't changed though. Used to be, prior to 1994, you could buy "high capacity magazines". Then after that 1994 "assault weapons ban" you couldn't any more. Then in 2004 when it expired, you could again. Then some states decided to ban the purchase of them at the state level, so you couldn't again. Then some states went on to ban ownership of them at the state level, so you had to (at least, were supposed to!) hand over the ones you already legally owned. So while rules are generally worse than laws with respect to variability over time, laws aren't always that great either!
The problem I see with AR (or AK) "pistols" is that they're right up there at the cliff edge of potentially being declared an NFA item by a gun-hostile administration. NFA violations come with some pretty heavy repercussions. Nobody with a brain cares if you rifle has an 18" or 12" or 36" barrel. But gun-hostile and NFA-supporting folks don't think rationally like that. This wouldn't stop me from buying an AR pistol now if I wanted one, but it's still something I'd keep in the back of my mind.