As is so often the case, I see that CSD and I have the same approach to cooking. I put the room temperature roast in a 325 degree oven, uncovered, and roast until the internal temp at the center of the roast is about 110-115 degrees. I then let it sit for a good hour or chill it overnight before slicing. This gives me a pretty nice evenly rare roast. It is perfect for roast beef or French dip sandwiches.
I read a story a while back in Cooks' Illustrated suggesting roasting an eye round at a roasting temperature of 225 degrees to an internal temp of 115 degrees, but have not yet tried this. This is supposed to minimize shrinkage and give you an even pink edge to edge. I have read other approaches suggesting putting the eye round into a preheated 500 degree oven, then turning off the oven immediately and roasting at about nine minutes per pound until an internal temperature of 115 degrees. I have done this with other roasts, and it only works with my indwelling temperature probe that allows me to monitor the internal temp from outside the oven. If you open the oven to check the temp, you are screwed, since you lose your residual heat that is cooking the roast.
Edited to add some details.