How to make browser request smaller range with 206 Partial Content

So I finally gave up on this and had a look at the source code of Firefox. At the place where Firefox receives a different range than expect, a comment is placed by a developer asking what to do in this case. The specification does not specify what to do in such case and so Firefox chose to do nothing. Chrome is a little more creative and came up with what the developers thought would be the best response (which is absolutely the result I want).

It seems like I am not the only one with this problem, otherwise I wouldn't have gotten upvotes. The thing is: to make Firefox correct this problem we would need to make a change to the specification which I believe to be close to impossible. Therefore I am closing this question and marking this post as the answer.