Hi John,
I am assuming that the car radio's amps are bridged without a transformer, with a + non-inverting amp and a - inverting amp for each speaker. Each amp's common is ground, not floating.
Since your circuits have the lowest value resistor in the - inverting side, their outputs are also - inverting, which is out-of-phase.
My revision of your circuit also adjusts the volume, but as an addition allows you to adjust for a + non-inverting or a - inverting output for a choice of phase, with a null position for extreme attenuation.