now I'm on a weekend:) No Solidworks on hand. But my first impression I would make the part using a Boolean operation because I think it will be easier to make your coil with its barbaric shape and then make a subtraction on a cylinder, what do you think?
In the idea it is almost that except that the diameter of the scan section must increase from the moment the pitch of the helicoid begins to vary. This is also when the helical becomes conical. Indeed, the back of the throat is constant. I'm attaching a step of the file as it is today. In fact, the only thing missing is the change of diameter on the variable pitch part. This should normally connect perfectly with the "end" of the gorge where we currently see a kind of shoulder.
Thank you for your help and have a good weekend to you too
Yes, I agree with you, only, we can't use a helical curve directly as a guide curve. And it is virtually impossible to create a second guide curve. Then to finish, it will be tense to calculate the Ø of each section, the step not being constant...