So this may or may not have worked, I don't know.
I logged into my Radegast client and did an inventory reload in a low-lag sim. Then I switched to Firestorm and presto, my inventory was back.
Hopefully this helps someone else.
This is exactly my problem too. I've submitted a ticket.
Interestingly, when I load Radegast (text only viewer) I see my full inventory. It just doesn't show in Firestorm or the vanilla SL viewer.