I just did a 5-minute check with Geometer's Sketchpad. In one iteration (original directions only) it didn't do too well. My angle was 75 degrees. My guess for placing D was BD/BA=0.292. The angle E'OB comes out to be 25.562 degrees, 2% high. I think my construction is correct because as the first guess approaches 25 degrees, the construction result does also. But I agree that further tweaks might make it much better.