State Legislature Method, or
the State Ratifying Convention Method.
This is the most important part of your post. Far too many people think of an Article V Convention as a declaration of martial law. Such a convention can only propose amendments. It can not put anything into effect. Even if such a convention tried to unilaterally impose an amendment or new constitution, how would they do so? Would the military back the convention's clearly illegal act? Would the federal and State governments acquiesce? Would the People not fight the convention's illegal act? There a much greater and realistic chance that an Article V Convention would be too divided to propose anything than that it would be unified enough to attempt a coup.