UPDATE:
I did in fact choose to take a dremel to the heatsink and slice off about an inch worth of fins, just like in the picture above.
Reinstalled the card and it seems to be working just fine. Looks like it is idling at about 50C, pushing 60 after a little load....unfortunately I didn't think to check the temps before the hack-job, but I would bet it was around that beforehand.
That seems like an acceptable temp for a fanless GPU to me! Not a gaming rig, just HTPC, so I'm not too worried.