Everyone is different. I often feel completely awake and alert just after going to the toilet.
You need to be awake enough to do the technique. If you can do 5-minute MILD after 30 seconds WBTB, that's fine.
If you wake up naturally often, just remind yourself of your intention and go back to sleep. One thing I found out is that future-oriented intention keeps me awake and future tense mantras make it into the dream but don't work. And it helped me a lot to switch to supersimple "I am dreaming".
You said elsewhere that you need to let your mind wander - I am the same. Let it. Don't worry too much about keeping dreaming on your mind as the last thing. I use the "I am dreaming" mantra very lazily and let my wandering thoughts overpower the mantra.
Also, experiment with it. Try to learn what works for you and what doesn't, what makes you sleep, and what keeps you awake.
I would say, for me, 80% of lucid dream induction is managing my sleep, keeping it not too deep and not too light. Sleeping, with high enough awareness but without waking up too often.