I know enough to understand it requires repeatable experimentation to support or confirm a theory, and that no experimentation or theory develops or takes place apart from intelligent design. Please correct me if I'm wrong, since you know so much about science as to judge my knowledge as absolutely lacking in this regard.
Well, repeatablility is only one of the criteria for a theory. And TToE meets that one. I have no idea what you mean by "no... theory takes place apart from intelligent design." That is a prima facie meaningless statement.
A very quick summary as what is required for a thoery courtesy Dante Alighieri :
A) Falsifiable - are scientists going to be able to potentially show it to be false?
B) Tentative - is it subject to change and incomplete?
C) Naturalistic - does it use natural explanations to explain natural phenomena?
D) Parsimonious - does it make the least assumptions possible and does it not unnecessarily complicate itself?
E) Make Accurate Predictions - Does it predict what we should see in the fossil record, in comparative genomics, etc.
F) Encompassing - Does it explain why predictions made by evolutionary theory are very accurate and why evidence supports evolution?
G) Supported - Are there many positive lines of genuine evidence for it?