That is an excellent explanation of a very complicated problem, in terms that we can all understand.
The KM added a fourth rotor on 2nd February 1942. It's traffic was known as 'Shark' to Bletchley Park and it was not deciphered for nine months, and then only after new and relevant key sheets were captured.
The fourth rotor was slimmer than the other three, was not interchangeable with them, and did not rotate during the encryption process. It did of course add an additional stage to the cryptographic algorithm. The reflector wheel (UKW) was also reduced in size to accommodate the extra rotor. The new naval machines (Enigma M4) had a choice of two extra wheels (zusatswalze) named beta and gamma. Which should be fitted on a given day was given as an addition to the monthly sheets. There was a setting on the fourth wheel (it was in fact 'A', the KM had A-Z rather than numbers 1-26 on the circumference of the wheels) which rendered the M4 machine compatible with earlier Enigma I and M3 machines, which were still in use throughout the Wermacht.
Cheers
Steve