Hi,
Well, the .corr file lists the stars we think matched between your image (axy) and the reference catalog... if you use the 4100-series index files, those come from Tycho-2 (
http://data.astrometry.net/4100/). If you include the solve-field --tag-all flag, it will carry additional columns of data from the index files to the corr files (eg, for Tycho-2 I think it's just mags).
If you want to just speed up the process you're doing, you could create a "kd-tree" file from the tycho2-cut.fits file --
startree -o tycho2-cut.kd.fits -i tycho2-cut.fits
and then, after you convert the x,y to RA,Dec via WCS (which you can do in a batch via the "wcs-xy2rd" program), you can use
query-starkd -T -R <radius> -r <RA> -d <DEC> tycho2-cut.kd.fits
for a search radius "radius" (in degrees).
(Or you could do one query-starkd call at the center of the image and with the image radius, (and write to a RA,Dec list with the "-o rd.fits" flag) and that will give you all the stars near your image, then you can do the process you described with just the stars that are nearby.)
cheers,
dustin