The thing is, the last part does not just explain the joke, it is a very angry rant, and it ruins it for me because of the change of tone.

Imagine in real life, someone starts making a joke, and then suddenly starts cursing and yelling. I wouldn't be comfortable with what feels like a lack of self-control and I will try to move away before things get violent.

Either do the "joke" style or the "angry rant" style, not both. The joke can be explained calmly if there is a need to.