How to convince a Doctoral Committee to accept me as a PhD student when I already have a PhD in a similar field?
I agree with your advisor that most people would consider that the purpose of the doctorate is to teach you how to be a researcher and another degree isn't going to give you anything you don't already have. And giving the opportunity to another student is a positive good in the eyes of many, possibly most.
Moreover, if your goal is to do research and get paid for it there are better ways to achieve it. You should put your efforts into those instead.
But, to answer your question, about the only way I can think of to achieve this goal is to find someone who has a project and a very specific need for assistance that only you can fill. Possible? Sure. Likely? Not so much. And you would be better off doing a post-doc with them in any case. The pay would be better. You would have an opportunity to learn. Etc.
There is nothing stopping you from learning even outside a formal program. It takes a slightly different kind of discipline, but no more or less than that of a degree program. You can also build a circle of collaborators to help you find interesting ideas that commonly come up in class/seminar situations. You should probably explore that option in any case.