Insomnia Support Group
Insomnia is a symptom, rather than a disease, and is characterized by inadequate quantity or quality of sleep. People with insomnia complain of difficulty falling or staying asleep, which results in significant impairment of daytime functioning. Insomnia is categorized as transient (shorter than one week), short-term (one to three weeks) or chronic (longer than three...

First, you likely have identified at least some of the basis for your insomnia -- depression and anxiety. Both can be potent fuels for insomnia. Therefore, by treating those, your sleep stands to improve.
What you don't want to do is take substances that unnaturally force sleep without also addressing the true underlying basis for insomnia. This would be something to discuss with your psychiatrist, and hopefully arrive at some sort of managed strategy that might includes both pharmacological and non-pharmacological treatments. If I were in your shoes, that's what I'd aim for.
You've listed a few ideas using sleep hygiene methods, which are helpful. You can check out CBT sleep training for many more simple, common sense ways to help yourself sleep.
Finally, you are so right about 'give me something to do'. This should definitely be a focal point. In other words, by filling your days with activity that tires you out both mentally and physically, you will do wonders to help yourself sleep at night.
Good luck and keep us posted.