The difference between a theocracy and an ecclesiocracy has to do with the source of authority and law. In a theocracy, God has supreme authority as Creator of the universe, and therefore, His laws set the standard of right and wrong/good or evil. Since God is the final authority, all of our rights and privileges come from Him.
In an ecclesiocracy, the Church has supreme authority, and therefore, they can set the standards of what's right or wrong/good or evil. Rights, then, would come from whatever the Church says, apart from the authority of God Himself. The problem with an ecclesiocracy is that even the Church itself receives its rights from somebody else (God), and therefore, cannot distribute rights to the people. Also, since the Church does not always possess perfect wisdom and understanding (due to its incorporation of sinners) to rightly handle human affairs, then it could have occasions where its decisions could gravely impact a society in a negative way. Thus, it would fail as an authority to rightly govern its people.
One thing you're missing is the transcendental nature of God by His Holy Spirit. God does still govern people by means of His Spirit, Whom changes the hearts of men as He wills. This is how a theocracy works. Sinful men are changed by the Holy Ghost, and given new hearts to understand and obey God's commandments, which influences their decisions on civil governing, morality, just laws, etc. God is omnipotent, omnipresent, and omniscient, which means He reigns over everything and possesses wisdom and ability to govern anything He pleases, according to His will.
America was founded on these principles of theocratic ruling, beginning in the 1600s with the Puritans. Sadly, we have lost our knowledge of what our founding fathers understood about the nature, authority, and legitimacy of governments (due to humanistic teachings in our public schools and Biblical ignorance in our churches). As a political scientist, I have to say that most people would be surprised at what our early engineers of American jurisprudence believed in relationship between God and government, because America was not started as a secular nation. Unfortunately, we are moving in that direction today, and that's why our nation has gone down the tubes.