What should a tenured professor do to move to a more research oriented school?
Its difficult, and rare for faculty to move from non-research oriented schools to research oriented schools, particularly at the senior level. To be hired as a senior faculty member, you generally have to be specifically recruited, and someone has to make a case that you, specifically, would substantially strengthen the department. This is because making an offer with tenure is a huge commitment for a department, and much more expensive than hiring a younger scientist. 

So what you have to do is be a visible leader in your field. When people think of your field, they should think of you, and when their university thinks of expanding their coverage of your field, you should be one of the first people they think of.