FatalError: Export ran out of memory while compressing a very large file. To successfully export, turn compression off by specifying the -nofilecompression parameter.So the really big .cmp/.cab files I was creating can't be compressed. The solution suggested in the error message is not attractive, since these are files that have to be transmitted over the network. My solution: cut the "-cabsize" parameter on the "stsadm -o export" command back to "60". The export ran to completion, the SharePoint Designer "Restore website..." operation was successful, and the site actually looks correct.
The one gotcha I saw had to do with the "60" (megabyte) limit on the size of the .cmp/.cab files. This particular site was exported as 6 files, with sizes (in order of creation) of 89, 86, 82, 64, 68, and 56 megabytes. Examining the contents of the 89MB .cmp file (by simply changing the file extension to .cab and double-clicking), showed that the last file added to the .cab was 47MB (an .mp3). Probably the export process doesn't look ahead at file sizes to determine when to switch to building the next .cab file, but waits to detect the occurrence of the overflow.
So admins migrating SharePoint sites with (even moderately) big files, beware!