Since you locked me completely out of the other Trinity thread, I do want to comment that I've been enjoying the discussion between you and Butch.
However.... As you describe "Hierarchy," I'm not sure you have the right adjective. There is no equality within a Hierarchy. A General, Sargent, and Private describe a Hierarchy, and these are not equal, even if they do have different responsibilities. Neither would a Principal, Teacher, and Student. Or CEO, Manager, Employee.
BUT, you did state that these co-equal persons of the Trinity have differing responsibilities. (If I recall you used the word "Roles" (?)) Given this, a Teacher of Science, a Teacher of History, and a Teacher of Math would be in essence "co-equal" but I wouldn't want my history teacher to try and instruct me on differential equations. And I sure wouldn't ask my Gym Teacher to help me with my Nuclear Physics homework.
Now you say you heard the term "Hierarchy" from the Holy Spirit. If that's valid, then you are not a Trinitarian, but something else (since it's not really Nick's role to change definitions). But if God were Trinitarian, He would not have used that adjective "Hierarchy" although at this point I'm not quite comfortable with recommending any specific adjective.
When Paul started to speak about different roles in the church, he staunchly ruled out hierarchy.
For the body is not one member, but many. If the foot shall say, Because I am not the hand, I am not of the body; is it therefore not of the body? And if the ear shall say, Because I am not the eye, I am not of the body; is it therefore not of the body? If the whole body were an eye, where were the hearing? If the whole were hearing, where were the smelling? But now hath God set the members every one of them in the body, as it hath pleased him. And if they were all one member, where were the body? But now are they many members, yet but one body. And the eye cannot say unto the hand, I have no need of thee: nor again the head to the feet, I have no need of you. Nay, much more those members of the body, which seem to be more feeble, are necessary: And those members of the body, which we think to be less honourable, upon these we bestow more abundant honour; and our uncomely parts have more abundant comeliness. For our comely parts have no need: but God hath tempered the body together, having given more abundant honour to that part which lacked: That there should be no schism in the body; but that the members should have the same care one for another. And whether one member suffer, all the members suffer with it; or one member be honoured, all the members rejoice with it. Now ye are the body of Christ, and members in particular. And God hath set some in the church, first apostles, secondarily prophets, thirdly teachers, after that miracles, then gifts of healings, helps, governments, diversities of tongues. Are all apostles? are all prophets? are all teachers? are all workers of miracles? Have all the gifts of healing? do all speak with tongues? do all interpret? But covet earnestly the best gifts: and yet shew I unto you a more excellent way.
(1 Corinthians 12:14-31 KJV)
(I'll slowly back away from the third rail now.)
Rhema