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Hi Allan
I have had consistent results from rotating the laser in a v-block such as a piece of angle iron or aluminium.
A V-block minimises play in any radial direction so that you can re-set axial accuracy while rotating the laser. I reckon I get to within couple of mm of dead centre with careful adjustment, via target at a few meters as you have done.
The eyepiece holder such as you are using might still have residual radial L-R slop under the single thumbscrew. Just the act of clamping could shift the laser.
When I find a good eyepiece holder in my various bits, I set it aside to use for collimation in my Newt. Once I know the laser itself is collimated, I rotate this 'best' EP holder with laser fitted, to check its own wobble. Good luck.!
& btw, my own preferred method for collimation is via Cheshire eyepiece.