SCOTUS addressed this very question already. Respectfully, the left sort of freaked out when it learned that it, too, can lose. However, freaking out about the Thomas concurrence ignores the fact that he is exactly one vote of nine, and the other eight are not interested in revisiting the issue. Even if you could get four to Grant cert, Kavanaugh has already indicated in his Dobbs oncurrence that he does not support overturning Obergefel. That's a shame, because that decision was crap law, but it is what it is.
This measure, too, is not the best way to handle this. We don't have a national law on cousin marriage, because it's left to the states, who are supposed to handle this sort of thing. However, it's better than attempting to find a friendly judge to impose your will I suppose.