Going top answer part of my own question, in case anyone is following/searching this thread.
The Pocket Outlook "Store attachments on Storage Card" option requires that the removable media (MMC/SD/CF etc.) be identified (named) "Storage Card". SD Cards, for example, are mounted with a "folder" name of "SD Card" and are therefore not recognised. There is a registry hack to change the name of the removable media, which is documented here
http://www.ppcw.net/?itemid=1885&catid=80
I noticed that I must have already done this on my 3870 in the long distant past and forgotten about it, since the SD Card mounts as "Storage Card" and not "SD Card" as it does on my iPAQ hx4700.
That having been said, attachments work on the 3870/WM2003 and are stored on my SD card (using the hack), but they still do not work in any manner on my hx4700/WM2003SE - so I must have messed something else up ... something which is eluding me at present.