I think there's something here, but I haven't figured out what or how to fix it.
Things I've found that have helped:
A thorough eyemask and good earplugs reduce the awakenings and help me sleep in a bit longer.
An air conditioner that runs into the morning to keep it cool - I think the air temperature warming after the sun comes up starts to trigger wakefulness?
Cutting out sugar and caffeine after 6pm, which helps getting to sleep a little.