Pls do everybody who wants to help you one BIG favour: indicate built year and month, model, has the car automatic or manual gear, which engine, and more other details. There are 7 series models such as E23, E32, E38, E65, E66.
And each of them has a special design, engines and country version.
Just use on top the user CP and indicate your model with details and it will always be in your profile, and if you do not know when your car was built, use my website and see under VIN decoder.
Sometimes even the month of a year is important to see what kind of MOTRONIC it has or which country version etc.
Also more details, the more the better:
did you check with a multimeter all the time the voltage?
what is it at engine off and ignition off, at ignition on, when cranking, at 1.500 RPM and at 2.500 RPM, as you say that solves the problem.
Have you checked the belt? Maybe slipping? Belt tensioner?
Go for the alternator checking first, DME seldom is damaged.