I found something weird (to me, at least). If I try the FIT, TIFF or JPG files I get from my CCD software, then AT fails to solve.
However, if I upload any of these files to Astrometry.net, get it to do a solve, and then download the "new-image.fits" file it supplies, then my local copy of Astrotortilla can solve on this in <10 secs!
So is it that AT doesn't like my file formats, and yet Astrometry.net can somehow handle them? Very strange. At least I know my local copy of AT is working fine -- just not with my file types...