Could U.S. citizens realistically abolish their state government, if that power is declared in their state constitution, but no methods are described?
No. There is no lawful way to abolish a state government in the United States. This makes it unnecessary to address the second question.
A critical point is:
All processes will follow pre-abolishment laws.
No state has laws that provide a lawful process for abolishing a state government, and neither does federal law.
The only way to amend a state constitution to change the nature of a state's governmental institutions (including removing some of them) is through the process for doing so under state law, or through a court declaring a state constitutional provision invalid under federal law or the U.S. Constitution.
This is true notwithstanding language of a state constitution, or under the Declaration of Independence, to the contrary. These provisions are best viewed as aspirational, or as validating the original historic decisions that caused the state to become part of the United States, rather than as authorizing future conduct.