Hello Go! I'm not too familiar with Effexor, but I do take Zoloft, so they do share some similarities as they are both SSRIs. I have an adrenal problem where I must take a drug that messes up my sleep, too. So, with all that said, I'll say a few things.
I take my Zoloft 3x a day to equal 300mg, a rather high dose, but that's what it takes to fight the side effect from the adrenal pill that depresses me very badly. Before the adrenal problem, I was told to take it in the morning. I will say this... Zoloft does make me a little sleepy, so I suppose you could try taking it at night and see if it helps!
As for the sleeping pill you're taking, you COULD try a couple diff over-the-counter sleep pills at the pharmacy, and see if one helps you sleep better, if that is your main issue. Also, you said your Effexor isn't helping you now either, so you should see your doc and ask for an increase in it, that you are feeling much more depressed now (you CAN get used to SSRIs). Hope this helps you out. GG