Call it abuse of the machine since it takes a lot of force to do it, and it should be disallowed because of that. Now, if there was a way to do it with a nice sharp shove of the machine you probably can't disallow it. It could be argued that a ball heading down an outlane can't be shimmied up, or you hit the side of the machine to use the side rail to make the ball safe otherwise.
The one person who is doing it is going to see it as picking on them specifically no matter what you do, and if they figure out a way to do it without banging the lockdown bar, how would you block it then? I'd argue that anytime there is a ball guide or something for the ball to interact with besides the apron, you would be allowed to influence the ball as long as you weren't into the abuse of machine territory (itself a slippery slope....)
If the tilt is that loose on that SBM you can 'twist' the cab as the ball is coming out of the kicker to go through the horseshoe to relight it anyway. That will become the move of choice then. (that one isn't even that hard to do).
The only thing that really makes it abuse of machine is that you have to hit the lockdown bar to move the ball.
You can just define in the rules that in the case of SBM being used in a tournament, the area allowed to influence the ball does not include the area below the flippers, near the kicker. (To allow the pins on the side to still come into play, since they are clearly there to percentage the ball path). As long as people are aware of the rule upfront, there it is. If they think it's that unfair that they won't play, well, that's too bad for them.
You could probably just say "no hitting of the lockdown bar vertically" or something like that, would probably cover it. There's really no reason to hit the lockdown bar vertically anyway, other than bangbacks or moves like you're describing. You can say "hands must influence the lockdown bar which also gripping the sides of the machine".
I can bet that the person involved will try to do it anyway and you'll have to depend on the others in the game to report it.