If your Sony is HDCP compliant (which I'd think it would be), I would hope that an HDMI-to-DVI cable would provide full functionality. If it doesn't, I'd be curious to know why.
You say that the component inputs are all in use - I assume that includes all three of the 990's component inputs such that you can't use the 990's switching to help out?
The firmware loader is a Windows-only app, but I'll have to defer to the Mac experts about any sort of Windows emulation options that would let it run (Boot Camp and an XP partition would certainly do it, of course, but I'm guessing you don't have access to that).