For me they start between 5pm and 6pm.
I can spend the day in front of my screen doing (almost) nothing or admin stuff. And then it kicks on and I’m (a lot more) productive.
The problem is that it’s around the time I have to take care of the kids when my wife can’t...
True, and I don't think it has anything to do with a personal biological<->time of day connection. The time of day that works for you is probably related to the contexts of what happen before and after in your day. The events which lead you into one mindset or another. So you could change your day to change what time of day it is, as well. You aren't "stuck."
I seem to have a pathological inability to get much done before midday/afternoon/evening/night (depending on severity)
I wonder if this is a belief I'm self-reinforcing by identifying as an "evening coder". I mean, I doubt there's a physiological reason for this. It's probably a matter of this being a habit of a lifetime that I've never fought back against hard enough.
You could try what worked for me:
Make a list of 2-5 healthy habits or routines that don't naturally fit into your current rhythms. Things like being an early riser, going to the gym in the morning, finishing all of your work before 5PM, and so on.
Then, pick 2-week periods to try them out, one at a time. For example, I always thought I was a night owl and and had delayed sleep phase syndrome until I made a deliberate effort to go to bed at 9PM every night for 2 weeks straight. The first few days were painful, but it's easy to push through when you're only looking at 2 weeks maximum. After those 2 weeks, I realized I'm a much happier, healthier, and more productive person if I go to bed at 9PM and wake up at 5AM, but it doesn't happen naturally.
Alternatively, you may discover that a routine doesn't work for you, but you're not losing much by trying it out for 2 weeks.
On average, you have about 4000-4500 weeks in a life time. It's worth taking some of those weeks to run easy experiments that could pay dividends for years to come.
That more or less describes my working patterns over time, too, including the addicted to stimulants part. When I was young, my most productive time of day was after everybody fell asleep. Now, it's before everybody wakes up.
This used to be me until 4 years or so ago when I started skipping breakfast.
I love breakfast, but not because I feel hungry in the morning so once I discovered this I started skipping breakfast.
I'm fully convinced however that a good number of people would become more productive if they did eat breakfast.
FTR: I often wake up extremely early (often before 04 for days in a row) and can hardly get anything except extremely simple work done after 2100 (even back when I used to sleep more normal hours.)
In the afternoon is when I can concentrate for 2-4 hours and do some intense work. Take a break after that, and iron out anything small before calling it a day.
It's also been my observation that this is how I actually want to work. I feel ready and able to tackle anything first thing in the morning, but past 1 o clock nothing I produce will be that much good and my productivity will be a shadow of what it was in the morning.
I work freelance so that's how I work nowadays, it feels like it comes naturally in a way that no other method I've ever tried does including pomodoro.