Yup, the HK is conservatively rated. Don't swallow everything you see or read on those ads and product brochures.
For an easier if not better evaluation, check out the back panel of both receivers and look at the electric power consumption. Check if the total audio output power claimed per channel adds up nicely with the input power. It should actually be less than the electric power consumption. One immutable law of physics is: you can't give more than what you took in. In class AB amps in virtually every HT receiver, almost half the input electric power is wasted as heat and the remaining is the one that results in the output power.
So for a 6 x 125watt gear, the electric consumption should be in excess of 1,000 watts. Does the yamaha gear have that electric consumotion rating?
Also, if your display has DVI input and you want to make use of that, I can recommend the Denon 2910 and higher, but at 40T plus receiver and speakers, you'd be stepping out of your budget already. I think there's a Samsung and Panasonic models with DVI but they'd easily eat about half your budget. I have yet to see a DVD player with 6.1 out.