Not saying non-24 is good for you, but for people unable to follow a 24-hour schedule, free-running sleep (which is what OP is doing) is vastly better than constantly pushing through sleep deprivation, when one's schedule allows for it.
Speaking as someone with non-24 myself (which is much more severe in the winter)
edit: after reading more closely, it appears OP has entrained to a 28-hour day rather than doing free-running sleep; 28-hour days are convenient in that the week gets sliced into 6 days and allows for a consistent weekly schedule. However, I suspect OP actually naturally gravitates towards a shorter day like 26 or 27 hours based on their napping patterns. I also wonder if they might even have more success with 24-hour days and regular exercise, as from their description it almost seems like the daily exercise practice which they started after the 28-hour day might be regulating their circadian rhythm to be closer to a natural day.
[1]: https://en.wikipedia.org/wiki/Non-24-hour_sleep%E2%80%93wake...
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.
I remember so many people in my life being skeptical about my claim that I naturally have longer days than 24h. Then ~6 years ago I actually tested it; my watch recorded my sleep, and it became obvious:
https://photos.app.goo.gl/rTh2vkEMPEiJXx5Y7 [time-asleep graphed on a daily 24h chart]
And only then did I learn what a non-24 was.
That's exactly what this pattern is trying to avoid. For people whose sleep cycle is longer than 24h, a "normal" rhythm makes every single day a jet-lagged day, and in the "wrong" direction (it's easier to travel west/stay awake longer rather than travel east/go to bed earlier for most people).
Human body can be really bad at adapting to unworldly environments to the point you totally break down.
I don't see anything problematic with TFA's 28-hour days.
In the winter I can do 12 hours pretty often. It's not always but every few years I get a few weeks or months of 12 hour nights.
I love sleep.
A few months ago I finally got a CPAP machine after getting a sleep study due to abnormal blood pressure patterns (my blood pressure wasn't dropping overnight on a 24 hour monitor). I can now wake up feeling alert and ready to go after 6 hours of sleep (even though I could use a little bit more); I haven't felt rested this way in the morning since more than 15 years ago in my 20s. I'm not particularly overweight, nor do I snore, so it's worth checking into if your sleep patterns tend towards abnormal.
You seem oblivious to the decades of research into chronobiology and studies into shift work, jet lag, etc.
Your loss.