I disagree with cdbeam. I think there will be some crosstalk between focus and an X/Y lens adjustment especially when the thread is a little stiff as it is when using tape to eliminate wobble. I am still an advocate for screw type adjustments for centration because as the lens is rotated into focus and periodically adjusted, the centration may have to be tweaked and a "set it and forget it" jig may be cumbersome.
Copper is a bitch to work with. I love aluminum, but it does not thread as well as brass. I don't think thermal mass or thermal transfer is a significant problem for these non-pointer bench style setups.
I do not think there will be any change in PO. I can't think of a mechanism for this unless the fixed mounting was so off that the diode output was being clipped. With 2-3 mm lenses that much misalignment should be causing a lot of beam distortion. But, we'll see.