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.