The jb3 transfer protocol does actually allow you to start a transfer from any point in the file. Here is my experience: I use linux as my primary desktop machine, and 'gnomad2' as my file transfer utility. For whatever reason, my particular usb controller and my particular jb3 do not get on well - I was getting random transfer failures (it would abort the transfer at a random point in the file). I spoke with the gnomad2 developers, and they couldn't reproduce my fault - their hardware 'just worked' - although they had had other similar bug reports. Their solution was "re-start the transfer" which would be fine if I was tranferring a few MB mp3s, but I had basically a 100% failure because my .wav recordings were so large! Long story short, I hacked gnomad2 to resume transfers from the point it crapped out, it was very kludgy but worked (I now use a winxp laptop with nomad explorer, and no problems now).
Anyway... where I am leading... if your file is only problematic in the first few seconds then you just need to skip past that, and download the rest of the wav file. Based on what you've said I'm optimistic of recovery. If you're using linux I can let you have my hacked-up gnomad2, and talk you through what's needed - pm me. If you're not using linux... I could probably do the transfer for you, again pm me.
Once you have everything transferred off the jb3 you do need to figure out what happened. Perhaps the jb3 was shaken too hard causing bad write; perhaps the hard drive is on its way out. If it were me, I'd be inclined to put a new hard disc in there - lots of info on how to do this in the faq (I think).
best regards,
stephen