Big Chris:I'd still run the HDMI to the TV, and use optical to your amp. You may not get audio gains, but the picture should be better.
HDMI should improve signal integrity. However I wouldn't worry about bandwidth. Over the net you're never going to get great pictures in my opinion, because there just isn't the bandwidth to deliver them and by the same token therefore you won't need a high bandwidth cable connection.
Or to put it another way, an 8MB broadband connection (most people's connection never actually reaches this but a portion of this depending on your distance from the exchange) running at full speed with no slow downs can deliver around 400kbs download speed.
I believe BBC HD uses 16mbs over broadcast or approx 40 times more than the maximum bandwidth availble over the net on an 8mb line.
Given most people can't achieve 8MB, I doubt BT transmit at anything like the top theoretical speeds so probably stream at a fraction of 400kbs.
Doesn't take a genius to work out relative quality issues of 16mbs vs probably 100kbs (guestimated) over the net ie approx 1/160th of the broadcast data rate.
Don't think this will change much this side of the roll out of superfast next generation lines in the region of 100mb.