I can see your point, and you are of course right.
The kind of density I had in mind though was a different one - I took the balls to be extended objects, and mentally considered the ratio between ball radius and tube length, ie which proportion of the tube volume is occupied by each ball. Since both are length-contracted by the same factor, this ratio does not change.
In my defense, I tend to have a tendency to seek out invariant quantities when looking at relativistic scenarios.
But I don’t think that’s what the OP has in mind, unless I’m still misunderstanding him. He is comparing the same circuit from the same frame, only with current off and on, and argues that because the electrons are in motion, the distance between them decreases, and thus there’s a larger net negative charge in that section of the circuit because there are more electrons in that same length of wire. He never mentions the rest frame of the electrons, nor the EM fields.
What I’m saying here is that the distance between the electrons doesn’t change just because you turn on the current, because the observer is still stationary with respect to the circuit; there’s no length contraction of distances in the wire in the observer’s frame. In other words, the total amount of charge is the same, it’s just that this charge is flowing rather than standing still.
I have, but I don’t think that’s what the OP had in mind, see my comments above.