I did free-running sleep for a while (I mention this in the original 28h day post), but decided on 28h days to weekly match other people's schedules.

I exercised regularly before 28h days, and my sleep was still chaotic with that. I didn't exercise daily though, it was hard to fit everything I wanted to do on a 24h day. Having longer days means I can fit more things, which I think is one of the reasons why I increased the amount of exercise after moving to 28h.

I also haven't read any research on this, I just did what felt more natural and logical to me.