I will add that any such website should probably wait until AFTER the court case is concluded. I don't know that it is dangerous to expound on an issue you're testifying about, but it SEEMS dangerous in that it would open the door for legal trouble against you... IANAL, obviously.
not sure if you should testify. If you do, remember that there are services to clean up your image on google ...
You don't even need to go for extensive SEO, as Search Engines may change their algorithms every now and then.
What you can do is, you can create a website for your professional profile where you write blog posts. In one of the blog posts, you can clearly explain your standpoint in your own words. Just link this website to your Linkedin and other social networks. This is important because you have to say in your own words what you want others to see about you, so as to nullify any false idea others may get on googling you.
The recruiter who is going to hire you will surely see the link to the website that YOU have listed and if he really cares about you, that person will read the blog posts. So you definitely have control.
Celebrities all across the world have to deal with stuff which might malign their image, every single day. And you can notice that many celebrities just give a clear statement in their own words and it works out well.
Finally, it comes down to the decision whether you would like to testify or not.