I have the same problem, and have been casting around for a solution to this for ages.
There do seem to be some possibilities:
a) Some/all HiMD portables support upload via USB, but only via Sony's godawful SonicStage software, and only in Sony's proprietory .omg/.oma format. There is/was a tool to convert these into .wav files, but the link doesn't seem to work any more - should be findable somewhere on t'internet though.
b) More promisingly, if you have a full size Minidisk machine with an optical out, you can connect to somethiing like this
http://www.minidisc.org/part_Creative_Soundblaster_MP3+.html which is obsolete now (though available on eBay for about £5),but should be equivalents that take an optical feed in from the MD, eg
http://www.creative.com/products/product.asp?category=1&subcategory=16&product=30. The soundcard market changes so rapidly, that you'll need to check what is available when you're ready to buy. Still limited to transferring at 1x speed, but at least this avoids 1 A-D and 1 D-A conversion on the way, so should sound a hell of a lot better.
Having said that, if you've got a HiFi MD deck, and a HiFi CD Recorder, recording them all to CD would be a PITA but might be the most productive way to go!