I appreciate everyone weighing in. My primary question was answered - if I want to do this, separate tickets will be ok.

As to whether I should divert to ATL to do this vs. a shorter routing in regular F.... Zorak hit the nail on the head for me. It is a long flight any way I go, and being able to lie down to nap or rest is an important factor for me to consider, even taking into account the age and design of the seat. The day will be gone. I will have either gotten up crazy early or will be arriving crazy late, so will be exhausted any way you look at it.

Thank you to everyone for answering my questions.