Update on rear sight: the Springfield Armory Adjustable Rear Sight 1911 fit fine with a little filing. Took to range and shoots too high, about 5" high at 15 yds. Issue is although it's adjustable, the rear sight is a tad too long so it touches the frame and can't be lowered any further.
Good news is found that the typical Novak cut sights (65deg angle) can fit the BDE III. Bad news is that it can't be as long as this rear sight.
I ordered 3 different rear sights from Brownells. Will update next week.