How can a phd student lobby against university wide publication restrictions?
Plan S is explicitly meant to change the publishing practices of researchers, and the business model of publishers. This comes after decades of half-measures that did relatively little towards open access, and nothing to prevent subscription costs from increasing. Therefore, it will be difficult to convince your university and/or Coalition S to accommodate the existing practices in your field. 

Some large American universities are committed to open access, irrespective of the field: for example Harvard, or the University of California. And the situation is evolving relatively fast. In this context, it may actually not be impossible to convince conferences to offer Plan S-compliant options. Lobbying for that would still be quite an effort: the first thing to do might be to contact well-known open access advocates in the field.