I am glad you enjoyed my response I felt this was the most interesting topic on this forum to which I could formulate a response, so I decided to post my take. I will attempt to clarify the position that your dilemma exists on a spectrum and is therefore not a mere dilemma. To do so I will continue to use the following example:

You see your child drowning in deep water. You don't think, you don't philosophize, you don't debate what it is you ought to do in this particular instance. You don't act to be fair, you don't obey god, you don't care how you feel, good or bad, or how it affects mankind. Instead, you jump in to swim to your child and rescue her. — god must be atheist

This case was used as an example of your autonomous moral system. In the most extreme case it would be you and your child alone. Here the only choice is to dive in a save her. However, if only a few variables are changed; for example if you had a friend who was a better swimmer than you, instead of diving in you might have them do it. In this case the acquired moral system will have an effect on the action taken. The degree of the effect will be changed by a variety of similar factors. In this sense your dilemma is not black and white there are many shades of grey. Therefore it exists on a spectrum where most moral decisions have aspects of both the individual acquired moral system and the autonomous moral system. This makes it much more complicated than a mere dilemma as each degree in which both systems have been combined must be taken into account.
To directly address:

the paradox of what seems to be moral behavior, yet the behavior does not satisfy any of the parameters set out as requirements for acting morally. — god must be atheist

It must be noted that in these grey cases the qualifying word completely would be added so that it becomes: the behaviour does not completely satisfy any of the parameters set out as requirements for acting morally.

To overturn the philosophers who proposed an all-encompassing moral map for humanity you would have to demonstrate that a significant amount of actions were sufficiently tainted by the autonomous moral system.

This is an act that no human would say "it is amoral, it is immoral". To all this is a truly moral act. — god must be atheist

If the action was done purely on instinct would it not be amoral? At least some conscious thought is required to make it a moral action. Although to others it may seem that the action of saving a child was heroic and was made based off that consideration. In reality it was amoral as it was done purely through instinct. However, if there was any conscious thought at all in the seconds that it took to save that child; then would it not fall in your first category as it was a decision affected by that person’s sense of morality? True the range of moral options are limited based on the persons biology. In this case not saving your own child is not an option, biological instinct will compel you. Instead the effort exerted or the method in doing so might be changed. Unfortunately this is the case for every action a human might take as they are limited by biology. These biological instincts can be over come and given time completely ignored, otherwise morality amongst humans would be universal:

Some cultures are abhorred by any one or more of the following things, and they teach morals against them: cannibalism, child- and wife abuse, murder, slavery, incest or inbreeding. Yet all of these features were integral, working, and in some cases, necessarily accepted features of to us known and well-operating cultures — god must be atheist

Although this all takes place on a spectrum and is not:

two horns of the dilemma that has created havoc among ethicists. — god must be atheist

Humans are limited by biology in the conscious and unconscious decisions or actions they can preform.
In summary actions made by a conscious individual may be assigned morality and actions made without conscious thought are amoral. Biology limits the scope of what humans define to be moral. Morality is sometimes mistakenly placed on amoral unconscious action because it is mistaken for a conscious action and this can be done even potentially by the individual in question due to faulty memory or other factors.

I apologize if I appear to be rambling I would be happy to clarify any misconceptions or answer any questions.