[bojan]

Thanks for your comments, I really appreciate them :-)
There is not much lateral clearance for mirror in the tube (perhaps 0.05mm, but not much more than that). So there is no space for anything as thick as masking tape I am afraid. . Maybe aluminium foil, or Teflon tape like the one used for plumbing? I will have a look...
The retention mechanism consists of three rings: one in contact with the back of the mirror, a spring (it is a tube ~110mm in dia, 0.5mm thick walls and 7-8 mm long. It is splinted by 3 long cuts, so that it can be compressed (not much. maybe 0.2mm by reasonable force) in length, and there are 3 pads that are in contact with the previous ring.
And the third ring has thread at the outer edge, it screws into the main tube and it is fixed in place with one grabscrew 1mm dia at the side of the main tube.
I suspect that the seat for mirror (I haven't removed it yet, to keep dust out) is not flat, this is the only explanation why even slight pressure from this mechanism causes astigmatism, as demonstrated with those pictures. Or mirror edge itself is not flat. The thickness of the mirror is ~10mm in centre (so it must be pretty flexible)
The mirror can be rotated easily now, but clouds are back over Melbourne so this experiment will have to wait..
And yes, I will try cheshire eyepiece soonest..

EDIT:
There is one more aspect of this mirror mount design that I noticed and did not like: When grabscrew is tightened, it forces the threaded ring in the opposite side (there is considerable clearance for this, 0.1 - 0.2mm or so)... And because of the slope of the thread (metric, 60°) this ring is therefore forced towards the mirror.
So I had to check the pressure on the mirror after tightening the grabscrew, and adjust the clearance in couple of iterations.
Anyway, this is not well designed. I think I will remove the grabscrew and apply silicon rubber to the retention ring on couple of spots, to prevent it from moving on its own. This way I will still be able to dismantle the mirror if the necessity arises in the future.