Hi Edit - I've had the same experience as you that we can have success with a different sleep rhythm to what is generally taught, if that isn't working anyway. Generally it is wrong what that doctor said: you will not nec. get sleepy by going to bed, esp. if you have a sleep disorder like we have with fibro, so sleep hygiene says try getting to sleep for about 30-40 mins., but then do NOT continue, get up again - exactly like you think is a strange technique: It isn't, it's exactly right. Esp. for fibro I've heard several times to do exactly what you did. For me this wouldn't work, I don't think, but I have other really strange techniques like a 1' cold shower, my secret weapon.
What I've found out this year is that if I get feverish-fluey at daytime that is ALWAYS tiredness and sleeping immediately (or as soon as possible) is best, and it doesn't affect my biological clock whether it's a 20-40' power nap or deep sleep for 2 hours. I wish I'd realized that before, but I listened too much to general sleep hygiene advice and not enough to my body. That's because no one has ever told me that that feverish-feeling is actually tiredness.
To me it sounds as if you are listening to your body well - don't stop doing that!
BTW: I make my devices go to night shift mode from 4pm to 9am, so I don't get blue light from them. And that doesn't affect me much anyway, apart from sometimes inspiring me to something, so I try to avoid anything interesting. And if I don't, then I just enjoy the freedom of doing what I like.