The key to the solution to this problem is the need to understand that for any helix of a given fixed constant pitch the helix angle will vary with increasing or decreasing diameter. This is the reason for the dip in the helix angle at the intersection with the long flank of the rectangular surface. To succeed with this you will have to use a curve from equation and unless you are absolutely brilliant at mathematics you will need an accomplished maths guru to accomplish this; but it can be done. There is a very slim chance it could be correctly achieved with geometry and most likely with a very complex pitch graph. I would be fascinated to see the construction of a successful model that is absolutely correct.
Actually, I had to think on it a bit, but I believe as the model shows it's 100% able to be made using pure geometry with no graphs or datum curves via equations. In fact, I was surprised at how few features are needed. 5 features total and 2 of those are "Evaluate Features" used to drive the # of coils and the overlap on that long edge. I can easily modify the number of coils by changing a parameter and the overlap will remain the same. I could easily change that as well to give me whatever overlap I wanted. The sides are all flat and parallel to each other, no "S" bend anywhere. The rounded corners ARE helical as you'd expect, but the pitch is equal all throughout the model. Spent maybe a day on it.
I have created an example using Curve from equation I would say it is approximate but you will get the Idea. Someone with good skills in Calculus would easily be able to make this perfect.
Sorry but the part was created in Creo 4.0 hope you can open it.