[savedbygrace]

Can all the citizens of the state constitute a legislature for this purpose and set the method of choice?

No, because the Constitution guarantees to each State a Republican form of government.

[Cheburashka]

Republican may mean simply non-monarchical or non-dictatorial in this context. I’m pretty sure the Founding Fathers did not intend the Federal Government to impose its own idea of the proper organization of state government on the states.

But again, something to think about.