How to balance sleep with Fajr, Tahajjud, and sunrise prayers?

Assalamu Alaykum everyone, I'm struggling to keep a good sleep schedule because of prayer times. I used to wake up just before sunrise to pray Fajr, then stay up and start work early. That fixed my wake-up time around 6 AM, which usually falls within Fajr time. But it's better to pray on time and at the masjid, right? So now I wake up at the actual Fajr time, but that changes a lot between seasons-anywhere from 3:40 to 5:40 AM. So I can't have a set sleep schedule. Now, I try to wake up about 30 minutes before Fajr for Tahajjud, then stay awake until sunrise, then sleep for about 1.5 hours (one sleep cycle). After that I get up for work, but I end up starting work around 9 AM, which feels really late. When I used to wake up after sunrise, I'd start at 6 AM and felt so much barakah during those early hours. All my best work happened between 6 and 10 AM. I really miss that. If I try to stay awake after Fajr, I only get about 4.5 hours of sleep (since I go to bed around 11 PM). I need at least 6 hours to function well. Any practical tips? Jazakumullah Khairan.