I have been using 1CLICKDVD and ANYDVD successfully for quite some time now. I generally make movie only backups, no extras or menus etc. Sometimes, when backing up a very large source (King Kong comes to mind), the backup video quality is poor. I assume this is because the compression is so high. Is there any way to perform a split from a dual layer to two single layer discs to avoid this issue? For selected source materials this seems to be the best compromise. Note my HP laptop, which is now 18 months old, doesn't have a dual layer burner so that's not an option.

Neither 1Click nor 1Click Pro will do this. When I deal with something like you describe, I either break over and use a DL or use CloneDVD2 to split the movie to two single layer disks.

If you don't mind putting in some extra time you could rip the full DVD to the hard drive using AnyDVD ripper and then using DVD Rebuilder to reduce it to a DVD5 and there would be almost none video quality loss. It just takes several hours, but worth it in the end on those very high compression DVDs.
DVD Rebuilder comes in a free version and a more optioned Pro version that is $29.95.