As your chain tension is probably close to proper I would advise you to first check that the wheel is centered in the triangle and the cog is lined up well with the chain wheel.

If the cog is not directly in line with the chainwheel (same chainline) then you may have left out a spacer or moved it from inside to outside the dropouts, and you should correct that before further steps.

If the chainline is OK but the wheel is not centered in the rear triangle, partially loosen the nut on the same side that the wheel is pointing away from center until the wheel can be slipped very slightly forward, then retighten the nut and test ride.

If the wheel is already centered then do the previous procedure to both sides, making sure the wheel is centered when you are done. It's a bit of trial and error but not something you need to do very often.

p.s. Never heard of the "old trackies' trick" and seems unwise to set as loose as possible. That would be too much pedal play for my taste. I've always mounted to a medium point and then pedaled to find the pedal position that has the least chain slack. I then leave it in that position and adjust the chain for just a bit of deflection.