I agree with your analysis.
"One of the main reasons is the fact that I like her."
Indeed it suggests there is more than one reason at the same level. But it doesn't imply these reasons are all in the same level, only suggests.
"The second main reason ... " suggests you have labeled the main reasons, the first, the second and so on.
"A second main reason ... " just picks one of the main reasons up.
However, personally I would not use the expressions you presented.
They sound confuse, and the listener has to perform all this analysis.
I would prefer to say simply:
"The main reason is the fact that I like her."
"Another important reason is the fact that she cooks well."
or "A second reason is the fact that she cooks well."
Not a native speaker
Student or Learner