I am still trying to envision why one would need a spacer. Putting the chainring on the inside of a double crank has always established a straight chainline. Redishing a wheel may change the rim position relative to the dropouts, but it does not move the hub. Check to see if there is a spacer between the cone and locknut on the drive side. If so move it to the left side to move the wheel toward the drive side.

With all deference to to Stevo's "10 years no lockring" fixie experience (I have only 2) I would NEVER ride a fixed gear without a lockring. I am hesitant even to try the bb lockring setup on a regular freewheel hub. I will stick with hubs having threads for a track lockring. I have both brakes and use them, but I also prefer to stop without them most of the time.