If I recall correctly...........
About 5 years ago I was tasked with securing a replacement aircraft for our FAR Part 133 D operation. While researching the Bell 412 I believe that the only variant that met the FAR requirement was the 412EP.
Between FAR 133, 27 and 29 you will find that the number of aircraft manufactured that truly meet the requirement are very few.
At that time there was one operator in Texas that had a 412 listed on their 133 certificate. After a short conversation with them it was said that they did not actually meet the requirement even though the local FSDO had approved the FAR Part 133 D operation.
I have found that Part 133 D operations are extremely misunderstood. Much of the confusion comes from the hoist manufactures that make hoists for just about every helicopter made. If you look around you will see hoists mounted on anything that can hover!!
As the regulations don't apply to Public Use aircraft they are free to mount a hoist on a light single and hoist all day with it!
Sorry I didn't answer your question, It's a great topic!!