Thanks for writing out some more information. It sounds like you already have a few great elements present for lucid dreaming. That you wake up naturally and remember waking several times during the night is great. I know this isn't SSILD, but since you have those brief awakenings where you're still tired in the night you could DEILD. When you have these awakenings you could possibly slip back into a dream and hang onto awareness so that when the dream forms you're already lucid. It's just a thought.

Drifting off can be a good thing. I think it's a matter of keeping your awareness activated a bit more. How many minutes do you think you are up before you get back in bed? You wrote, "I have a drink of water or chocolate milk then head back to sleep." How long are you out of bed for? If it's not quite 5-10 minutes, maybe you can try spending just a little bit more time out of bed so you won't feel so foggily sleepy so intensely.
If you haven't tried, maybe spend a few minutes a few times a day cementing your intent to remain aware for the proper amount of times throughout the SSILD cycles. I hope this helps! Some other members may have some good input here where I fall short or simply don't think of some things.

If you can think of any other relevant details of your sleep, dreams, awakenings, etc., feel free to include those as well. You can do this! Don't give up and stick with it.

Oh, one more thing. Frustration can be a big hindrance to getting lucid. Try to think of each attempt as a step towards lucidity and something to be thankful for. I know this feeling as I have been there, but it does nothing to help.