Knowing that rescaling/remapping reduces picture quality I suppose that remapping a 1080i image on a full HD TV (1920x1080) in order to get overscan, will reduce picture quality because only part of the available source pixels will have to be redistributed on the screen pixel raster. Even changing the image amplitude (in SM) with 1:1 mapping will introduce extra PQ reduction, right?

Yes.

Does your display offer a cropping instead of an overscan option?? This eliminates rescaling and just blanks the outermost pixels.

It only has overscan on/off. When "off" it maps the 1080i output of my HD cablebox to the native 1920x1080 pixelgrid of the Plasma TV. The pannel is just filled up then. So I suppose there is no rescaling involved (at least in the TV). What still puzzles me however, is that even for the 1:1 mode I can adjust the picture size (in the SM), which again introduces a slight over or underscan and thus rescaling is there again...