I still have the occasional night of sleeplessness. The times that I've dealt with it in the past is to try to be ordinary by sticking to a routine that matches what I think is good sleep and good wakefulness. Being ordinary is a good way generally, I find, in dealing with things that seem extraordinary seemingly requiring an extraordinary solution.
Afa the benefits of sleep goes I have found during times of bad sleep that staying in bed and resting as much as possible for an ordinary period of time is sufficient for me to try to do ordinary things during the day. I've found it takes practise and that the practise pays off.
It helps to go to bed on a light stomach by eating early and or light. Keeping atmosphere to a rhythm that matches natures. Pink and White noise can be helpful. And other stuff. In time things seem to normalise which is nice because it leads to a better ability to deal with other stuff.