I have tried crushed and milled at the beginning of the mash, end of the mash, and crushed plus coffe-like process, then added at the end of the boil.
There is definitely a difference when using no lodo and adding them at the end of the mash or end of the boil vs at the beginning of the mash.
When I combined lodo with milled/ beginning of the mash, beer turned out similar to when adding them at the end of the mash (that is, the oxidation went away)
The advantage of adding them at the beginning of the mash is that you can account for the pH drop and add less acid. When adding at the end of the mash after mashing at 5.3-5.2, pH can get into the high 4s, and beer pH at or a bit below 4.0. Beer is ok but not great, too acidic.
Just did a porter and a dry stout with lodo and grains mashed together and they both turned out excellent, with beer pH around 4.3-4.4.
I am personally convinced that milled is the same as crushed with crushed just getting better efficiency. I am dialed in now with milled, so will just spend the extra cents and mill them together.
As a side comment, many German textbooks recommend a protein rest for dark base malts (ie Munich type) because of the higher protein content they normally have, but this depends on the malster. The last few years, Weyermann Munich has been similar or 0.5% protein higher vs pils, so skipping protein rest should be ok.