Relativistic explanation of attraction between two parallel currents

As far as your comment goes, you mean there is an absolute symmetry between the 2 wires. Maybe, but one thing I must tell you that when you are considering the electrons in WIRE 1, the relativistic effects will be as follows:

1. The electrons in their reference frame will consider the protons IN WIRE 2 to be in motion.
2. Then due to relativistic length contraction, the electrons will observe that WIRE 2 has a higher positive charge density. So the electrons will face more Coulombic attraction from the WIRE 2 than repulsion from the electrons in that wire.
3. Most importantly, where I think you are going wrong, the electrons in WIRE 1 will NEVER see the protons in WIRE 1 to be MORE as you say. That is, electrons in WIRE 1 will see that WIRE 2 has a higher positive charge density than WIRE 1 always due to special relativity and nothing else. On the other hand, in a similar fashion, electrons in WIRE 2 will see that WIRE 1 has a higher positive charge density than WIRE 2 always due to special relativity and nothing else.

Hope your doubt has been resolved.