It might be helpful to have sleep tracking to have a better idea of what you need.
There's hardware like https://dreem.com/en/product that promises to help people sleep better.
General tips for better sleep are about avoiding blue light right before bed. I sat my f.lux so red that green and black became the same color. In addition I have Philips Hue lights that dim red.
Cool down the room when you are sleeping.
Make the room in which you are sleeping pitch black.
Don't eat anything 2 hours before going to bed.
An off-label use of fluoxetine (Prozac) is that it can caused prolonged sleep, possibly by reducing anxiety in ways that make it easier to stay asleep longer but specific mechanism of action is unknown. Worked well for me in treating narcolepsy-related sleep depravation, i.e allowed me to stay asleep 10 hours a night so I got enough sleep to avoid sleep attacks during the day. I'm no longer on it and still able to get enough sleep; my theory there is that regular meditation replaced the need for a drug to produce the same effect, allowing me to stay asleep longer.
Methods I've personally found useful for improving productivity when temporarily my cognitive ability or conscientiousness is lowered, not necessarily due to sleep deprivation:
You seem to assume that your lowered ability is caused by sleep deprivation. Is that an assumption? If so, I would encourage you to track your sleep quality and your cognitive performance and see if they really correlate, if you can think of a way to do it.
My fully subjective impression is that my insomnia never impacted my cognitive performance. I used to stress about it impacting my bodybuilding. Then I started believing that the impact of my sleep deprivation is minimal, if any, and that new belief probably helped me improve quality of my sleep.