The EOR is a tough cut, and is also very lean. I've had it roasted. Wrapped in bacon, put in the oven on high heat for I think 27 minutes, and then turn the oven off and let it roast for 'n' amount of hours. I don't have the exact numbers, so you will have to google. Since it is tough and lean, why does it come out nice and tender? I always thought that tough lean cuts of beef, it was difficult to tenderize without braising it in a liquid.
They sell eye of round steaks here. There is a part of that muscle that is more tender than the rest, and it's edible dry cooked like any other steak.. It still has lots of chew on it, but the other parts of the EOR are not chewable.