I give up
You are making this way more complicated than it is. Fatal_Bert posted the pertinent part of the law above. The bump stock does not meet that definition, and that's why the ATF ruled the way they did - not once but twice.
1934 law vs 21st century technology...
OK, so in a previous life I probably was one of those people arguing about how many angels dance on the head of a pin... Guilty as charged. At least 50% of my argument is playing devil's advocate.
And to be perfectly clear, if I was king for a day, every single gun control law on the books would be null and void. I see no reason that law abiding citizens should be restricted in any kind of weaponry at all. The whole purpose of an armed citizenry is to offset the potential tyranny of a government military or police force that has exclusive access to more advanced weaponry.
However we are talking about an agency that somehow thought moving a pistol with a 'brace' on it from your forearm to your shoulder somehow magically made it into an SBR.
You can't simply look at GCA-68 as etched in stone, since many 'rulings' and 'ATF letters' have expanded and constricted that law over the last (almost) 50 years.
With the ATF and 'machine guns' they have been somewhat consistent.
1) You can't have some kind of motorized activation is one. This was just shown with the denial of the motorized glove they just denied.
2) Any kind of trigger manipulation that results in more than one shot being fired is a 'machine gun'.
I honestly think that my interpretation of the ATF's past rulings clearly show that a bump stock changes the definition of a 'trigger' on a gun equipped with one, since the original trigger no longer fits that definition.
It doesn't fire the gun, and is not involved in anything more than the mechanical linkage of the real 'trigger'... The bump-fire stock itself.
Not only is this logical and consistent with their previous rulings on similar matters, it has a very real, practical purpose.
The NRA was smart in deflecting the legislation that multiple gun grabbers and RINOs supported, by shifting this into a regulatory versus legislative arena.
Is it 'right'? Of course not. But we have to play the cards we're dealt. And with GOPers climbing all over themselves to 'ban' bump fire stocks, we'd end up with one of the biggest gifts we could give the gun control industry.
We've seen the various laws that have been proposed, and they are all back-doors to setting the precedent of arbitrarily banning certain accessories as 'too dangerous' for any citizen to own. As many folks here have pointed out, this would easily include any kind of trigger. But it could easily be extended to magazine bans and other 'slippery slope' items that Pelosi was (for once) honest enough to admit they would love to push forward.
Bump-stocks could have been designed to prevent any kind of action faster than an unmodified rifle. The ATF dropped the ball on that, and if they have to eat a bit of humble pie and reverse this, it won't be a problem in my mind, and it won't negatively affect the actual laws we have to deal with.
Back to the personal side, I really wished that the leadership of the House and Senate gave a big FU to the gun grabbers and passed the SHARE Act just to get their goats, but as we've seen the GOP is mainly a bunch of spineless wimps.
Our best-case scenario here is to isolate the problem (bump stocks) and eliminate them as a political issue in a way that the GOPers can deal with. They may not be ideal, but when it comes to 2A issues, they are better than the alternative.