electromagnetism - Relativistic charge density in a closed loop

When charges of conductance are at rest, there is an average distance between them. The relativistic origin of magnetic field says that distances between electrons shrink when they are set into a motion (we get current). This means that the electron density is increased while total charge is conserved. I just try to relate the contracted distance between electrons with the conductor, which stands still and does not contract.

If we had infinite-long wire, we could borrow any amount of charge from the edges of Hotel Infinity to increase the electron density without increasing it. But, real wires are of limited length. So, condensing charge -*--*--*--*--*--*- => -----*-*-*-*-*--- cannot make one segment more dense without depleting density in the other parts. I cannot make the whole wire more charged (and keep it neutral in the lab frame, at that). The same applies to the loop.

 * - * - * - *      
 |           |      * * * *
 *           * ==>  *     *
 |           |      * * * *
 * - * - * - *       

Here alternative physics draw a nicer picture to ask the same question

The image says that the loop of electrons shrinks as they start to flow. Yet, mechanically, electrons do not escape the solid wires, which stand still and do not contract!

That is the question: how do inter-electron distances shrink without leading to logical absurd?

This question stems from understanding why loop with current stays neutral, despite the electron density increase. I first guessed that the conductor stays neutral because positive charges flow symmetrically in opposite direction so that relativistic charge density increase in both directions compensate each other and keep the loop neutral. In this case the conducting loop would contract proportionally with the loop of electrons but it would not stay at rest in this case. Yet, the problem is that the loop of wire stays at rest and does not contract.

Answer

I was told in the paradox of conductor's neutrality and this is confirmed in Follow-Up #2: relativity and charge density that in addition to contraction, mentioned in the relativistic electromagnetism tutorials, the electrons of conduction experience an expanding force, when accelerated. That is they see that the distances between them stretch out in their proper frame, as they experience the acceleration. The expansion is natural for non-rigid bodies, as explained in the Bell's spaceship paradox.

I emphasize this since it is absolutely counter-intuitive for any layman like me, who are taught that moving train is contracted w.r.t. stationary observer. It is underspoken rigidness of the train that prevents it from expansion in its proper frame, so the train shrinks indeed in the stationary frame when accelerates. But, spacing between electrons of conduction is not tied rigidly, so, when electrons experience acceleration, they also see that the distances between them increase. The expansion factor is exactly Lorentz $\gamma$, which exactly compensates the contraction seen from the stationary station. The net effect is that distance between electrons is not changed in the lab frame. So, maintaining neutrality also eliminates the paradox of wire neutrality.

Though I still do not understand the source of the expanding force (which energy does support it?), the paradox vanished. Might be this also partially answers the Relativistic origin of magnetic field.

However, one thing is still not clear. If electrons see their chain expanded while loop contracted then how do they fit into the loop? I guess that it's a famous ladder paradox. Yet, it is in a loop now and since my question is exactly about this case, I would like to resolve it also.