I have had no troubles using HDMI-DVI adapter with a Dish VIP-622 DVR and a Denon DVD-1910 DVD player, previously running through an Outlaw 990 (for sale, PM me). The 990 has DVI ins, the Denon has DVI out, the Dish box has HDMI out and the TV has HDMI in.
I've been using various adapters on the ends of HDMI cables, as well as HDMI to DVI cables (i.e., a different connector on each end, no adapter).
I'm now running through a Monoprice HDMI switch, again using some adapters based on my cabling, and again, no problems.
Now, I do have some trouble going DVI out of my PC and directly into the TV's HDMI input. But that's more about the TV and the resolution of the PC itself, not the cabling or adapters.
I think you will be OK -- give it a try with a short cable and see how it goes. Monoprice and others have them for about $10 IIRC.
Good luck!