How do you start a persuasive speech on something that is rewarding to you?

Strange as it may sound, it can be harder to write a persuasive speech on a topic about which you are passionate, compared to one where you have no personal stake.

The reason is that the target audience is usually the kind of person (you may imagine) who does not have particular interest or enthusiasm for the topic of the speech, and is waiting to be convinced one way or another. If you yourself feel the same way, then it is easier to be objective about the strength of the arguments in favor of the position.

Conversely, if you are yourself a supporter of a cause, it can be hard to "step outside" that viewpoint into the mind of a non-supporter, to understand their point of view. (Hard, but not impossible.)

Start, then, with the mindset of someone who doesn't have a strong view about the topic: from that person's point of view, ask "what is in it for me?" or "why should I care?", "how will this make things better?"

If you begin with that person in mind, build on common ground, and structure your arguments to build up to your best argument (never lead with your best), that's a good way to look at it.