Change the main backbone of an application (2 - 3 weeks) in order to facilitate the upgrade of the application from AngularJS to Angular (which they tell us is going to happen...eventually) or, rewrite the application (~4 months) in Angular. What arguments should we be using to get the rewrite? Our pleas are falling upon def ears.

I think the problem is as you stated the first option requires less effort and to management achieves the same result. To them the option you propose is more costly you need to prove that this is not true. Look into the phrase "technical debt", essentially the changes you do now will require future changes to truly have a maintainable system. One day this technical debt will build and turn into real dollars, the software you are working with will be unmaintainable and slow which will mean they will need to rewrite it. I think recognizing this as soon as possible will prevent you from building more technical debt then can be handled by your team.

@Axis

So...fun story...That argument has been met with "But you said this would reduce technical debt" ...things stuff and more things. So a few years ago we had this application written in a home rolled javascript framework. We talked at that time and used technical debt and got them to agree to the rewrite in AngularJS. Since then, Angular has really taken off, and all of our new [frontend] stuff is written in Angular. We have even done some work to make the application a hybrid app and are adding new features to the application in Angular.

@coder-guy I guess that's the problem with js and frameworks once you move onto a "stable" framework it ends up getting replaced in a few years. I see where they are coming from then if you promised that this would be the solution to remove technical debt and were only met with the same problem again. I guess the lesson here is when working with web technologies I would never preface that any solution is final and always leave the idea open that in the future to be with the latest technologies a rewrite will be necessary. Hopefully with this in mind you can write your code in a way that is as framework agnostic as possible making this port from one framework to another easier. And rather than it being the solution the rewrite is part of the ongoing solution to stay current