You are correct with regard to the end cutting edge angle. The books reference the tool axis so if you wish to define it that way in your model then that would be in line with the books and I would encourage you to do that.
Now, let me tell you why I define it the way I do. The many, many illustrations and discussions in the books have confused and confounded machinists and would-be machinists for decades. You can see the drawings and you can read the terminology used to describe each feature but translating that into actually grinding a tool from that information is not easy. You have multiple tool faces, each of which angles in two planes, and the angles change with the material the tool is used with. If you went to a trade school the instructor would tell about all of this but then he would show you how to actually grind the tool. The hobby guy doesn't have that advantage. He has the books. This has turned the majority of the hobby machinist population into a source of carbide insert tool buyers and users, largely because it is easier but also because that is the way the industry has gone so it has to be better, right?
What I've tried to do in everything I've written on this subject is to simplify it as much as I could. I tried to define the what/where/why/how/how much for everything so that the average guy could grind a tool of his own, by himself, simply by reading what I wrote. And I used Mikey-logic to do it.
For example, the side cutting edge angle and end cutting edge angle of the Square Tool is what it is because it is intended to allow you to access a shoulder. The shoulder itself is 90 degrees but an included angle of 90 degrees on a tool will rub so I made it less than 90 degrees so it wouldn't rub. I used the side cutting edge angle as a reference so I could tell the guys to make the included angle at the tip less than 90 degrees; the precise angle is not important. To grind that angle, the simplest way is to use the side cutting edge as a reference and draw a line that is less than 90 degrees to it and then grind to that line. Simple, easy to understand. I chose 80 degrees because it allows a 5 degree cushion between each edge that the eye can easily equalize in that corner when orienting the tool. Mikey-logic, you see?
I have taken other liberties beyond this angle thing. I have tried to explain what each angle does and how they can be modified to allow the tool to work better on a small lathe. That is a major departure from every reference text on tool grinding that I am aware of. I am probably the world's only proponent for small nose radii; every other resource and anecdotal opinion will tell you that bigger is better (but they don't tell you why).
I hope this clarifies this for you. Okay, okay, I went beyond clarity into diarrhea of the brain but it was important to explain that I had good reasons for going beyond the texts.
At least now we have guys who can actually grind real lathe tools - good enough for me.
