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...

If you are not getting answers you need, you might consider asking your doc for a referral to someone else. Especially regarding insomnia, you might benefit from talking to a doc that specializes in sleep medicine.
That said, you are right there most definitely is a correlation between insomnia and depression, although the direction of causality isn't always clear. Are we depressed because we can't sleep? Or do we have insomnia because we are depressed? Little of both?
I do suspect that by treating the root cause of your depression, which often are underlying patterns of recurring thought distortions, your sleep may improve. And rapidly. Check out cognitive therapy methods, if you haven't already.
And Curious, if you can hear yourself snoring then that ought to be at least some reassurance that you are at a minimum deeply relaxed, which will work to help to refresh and rejuvenate you. And probably lead you into the deeper, even more refreshing stages of sleep.
I suspect you'll be helped lots by counseling, if you're not getting that now. Getting to the root beliefs and underlying assumptions of your negative thoughts and attitudes, then doing what you can to change them for the better, I suspect will probably help you a lot.
I will say that it is refreshing to hear that a non-psychiatrist will NOT prescribe anti-depressants. I would advise you to look for another psychiatrist and get evaluated for a mood disorder and get separate treatment if any are present.
I believe my psychiatrist would be interested in and trying to assist with both conditions that you have mentioned. At least he would explain what he can/could not do and why.
Don't give up!