It has been many years since I adjusted a 415 or other in the family, but pretend you are adjusting the discriminator of an FM receiver. With a scope, a 1 kHz oscillator driving an active speaker (or amp + passive speaker), adjust L1 for max amplitude, and L2 for lowest distortion. Speaker output needs to be high enough to get a decent waveform, but don't clip. If I recall, the coils are interactive, so go back and forth for best results.
To check noise, If you have a good, very quiet (<1uV), external power supply, try it and vary the voltage between 8 to 12V and see if the noise is lower at a particular voltage I suspect 12V will be fine and that the problem is with your supply. Get a copy of the Sennheiser power supply schematic to make sure you are feeding the mic correctly.
If I recall, their noise spec was 1uV! I was never impressed with PSC equipment. I built some battery supplies for these mics, and at that time, used LM723 chips as the quietest, and had to select between brands for who had the quietest. LM 317 or LM7812 are too noisy. Today, I'd use an LT3045 (0.8uV), powered by 2 x 9V batteries in series. If you just want to buy a supply, these are the kind I made, still available on eBay:
coherent communication microphone ps3 power supply - Tested | eBay. I have not made these in years and have no connection to the seller.
Good luck!
Ivan