Thanks for the pointers Chronon. I've now established that iTunes
is writing to the file's id3 tag rather than the iTunesDB, and it
is apparently using a standard id3v2.2 tag.
Using
ID3 Raw Tag Viewer I can see that the
bad tag generated by iTunes uses the ID3v2.2 tag
TPA, and looks like this:

Multi-disc albums with these style tags sort and display like this in the Rockbox database browser:
01. Disc One's First Track - mm:ss
01. Disc Two's First Track - mm:ss
02. Disc One's Second Track - mm:ss
02. Disc Two's Second Track - mm:ss
etc
If I re-tag copies of the same files with Tag & Rename, it looks like this in ID3 Raw Tag Viewer, it uses the
good id3v2.3 tag
TPOS:

And then displays and sorts properly, like this:
1.01. Disc One's First Track - mm:ss
1.02. Disc One's Second Track - mm:ss
2.01. Disc Two's First Track - mm:ss
2.02. Disc Two's Second Track - mm:ss
etc
As far as I can find, Rockbox claims to support both id3v2.2 and id3v2.3 tags. So what is happening here?
Is the TPA tag somehow malformed? Can anyone confirm or deny this from the hex example?
Or is it a valid tag but the Rockbox id3v2.2 parser can't cope with it?
Happy to supply example files on request if anyone wants to test themselves.
I really, really don't want to have to retag many thousands of existing files, and switch to using a different file tagger just because of this. Unless I absolutely have to after exhausting other possibilities!