It would most likely be during bottling. Even if your being gentle and avoiding splashing you can't prevent air/beer contact. I bottled for 10 years using the exact same procedure that you do. I just accepted that mild oxidation was just something I had to live with. My beer was still OK-->Very Good, although as
@Yooper mentioned the flavor was often muted, sometimes stale. But it was never too sweet to drink, even when gravity finished a few points high. So, there has to be something else going on.
I think your only option is to take what you learned and brew it again. And be sure to let us know how it turns out.