I went through this when I was trying to solve my cold starting issues. I too would rock it in gear and it seemed to help. I never did figure out how that was even possible. I ended up replacing the ground, and the starter (more powerful one as mentioned) and the relay etc etc. The good news is, it solved my problem. The bad news is, I'm not really sure how or why.
As for the battery, I would take it to a shop (took mine to Walmart of all places) and get a proper load test done on it. Voltage sitting doing nothing is one thing, under load is totally another.
I realize THIS is on another board but it does reference back here too. It shows other threads related to this issue (including Wayne's starter thread) and you may find something that helps.
I wish you luck with your issue. Trust me, I know how frustrating it can be.