Mike,
Regarding baptizing one's self, NT baptism is in the likeness of Christ's death, burial, and resurrection (Rom 6:3-5). I don't think anyone would contend that Jesus crucified, buried, and then resurrected Himself. He submitted to death at the hands of others, was buried by others still, and was raised by the power of God.
NT baptism, IMO, would be dependant upon submitting to baptism administered by a second party. I know of no NT authorization for anyone baptizing themselves.
About the administrator of baptism and their understanding being essential, I would say that if one desired NT baptism, but only had access to one who was not a Christian to perform it, then it wouldn't be the first time that God had used someone who was ignorant of His will to perform His will.
Case in point: The Crucifixion.
Jesus' rejection by the Jews, and subsequent crucifixion were all part of the "determinate council and foreknowledge of God" (Acts 2:23). Yet, at the same time, Jesus said, "they know not what they do" (Luke 23:34).
Neither the Jews, nor the Romans knew the significance of Jesus' death, yet it all went according to God's plan. His will was done.
The ignorance of the Jews and the Romans did not negate the efficacy of Jesus' death. Thus, I would conclude that the ignorance of the administrator of one's baptism would not negate the purpose of that one's baptism, provided they understood the purpose themselves.
In closing, let me say (and I think I can speak for any Christian) that Alexander Campbell and the others involved in the restoration movement are not the standard by which we determine right and wrong.
Those men did the best they could to free themselves from denominationalism, and return to simple NT Christianity, with the NT as their sole authority for doctrine and practice. That is a noble goal, and we applaud them for the success they had, and the example they set for those who share that goal.
I'm sure that there were some false doctrines they may have had a hard time loosing themselves from. I know I have had to unlearn many things since leaving the Southern Baptists.
Phil 3:15-16 comes to mind. It reads,
"Let us therefore, as many as be perfect, be thus minded: and if in any thing ye be otherwise minded, God shall reveal even this unto you. Nevertheless, whereto we have already attained, let us walk by the same rule, let us mind the same thing."
If I were to chance a paraphrase, it might read, "If you are mistaken in some areas, keep studying, and make changes when you realize they are needed. Do the best you can with what you know."
Of course, back then there was miraculous knowledge, which is not available today, but we have the Word of God which we are commanded to study (2 Tim 2:15), and if we do so with honest and good hearts (Luke 8:15), we will come to the unity of the Spirit (Eph 4:3).
In Christ,
bmerr