I've gone through this with my pedals. What I've concluded is that it's more important to me that my knees track up and down and not wobble than to be centered in the pedal.

With that said, over the years before I got my pedals, I've taught myself to ride with my knees near the top tube and not pop out on the upstroke. At first, I used cleat shims and now I don't. When I do shim my left foot, my PCO moves from 6mm outside to nearer the center but not always perfect. Sometimes it's inside of center. When I don't shim, my left PCO is anywhere from +6mm to 0mm and I don't notice any difference in power production, comfort or aches afterwards. My right foot is mostly near center all of the time.

When I used to move the pedals from bike to bike (Road and Tri) they read differently for each bike despite using the same shoes. Now I have 3 sets between my Road, Tri and Track bikes and they all read different even when using the same shoes so I don't really worry about it as long as my foot feels straight and my knees don't wobble.

Something that might contribute to this is I don't ride exactly centered on top of my bike. I always lean slightly right and I don't know why. I know I do this because I can always see the right side of the front wheel and it takes effort to see the left side of it. Years ago I thought my frame was crooked but when checked it was perfectly straight, and now every bike I've had is the same way. It's just something I do and it may contribute to the pedal offset.

You can try playing with changing the centering of your shoe on the pedal or shimming the cleats if you feel it's a problem but I haven't needed to. Also, I use the Look Black cleats.

Thanks for your comprehensive reply; appreciated.

Another thought I had is that I haven't compared the Q-factors between the bikes.

On my road bike I'm using an FSA Gossamer Mega-Exo
Tri bike has an R7000
Track bike has an Origin 8 with a UN300 107mm BB