Hold on, there is additional info on radeon IRC log (and in OP's head :)) which
is not yet in the ticket:

>radeontop output of stuck card:
>gpu 100.00%, ee 0.00%, vgt 0.00%, ta 0.00%, sx 0.00%, sh 0.00%, spi 0.00%, sc 0.00%, pa 0.00%, db 0.00%, cb 0.00%

The above is only when no load on the card... when running a 3D app the gpu bit
stays stuck at 1 (100%) but other bits behave normally. 

I think that pretty much eliminates the caching idea.