You can use more than one alarm clock or make the waking sound louder. Have you tried autosuggestions?
The BIG WBTB Topic link: https://community.ld4all.com/t/big-wbtb-topic-summary/22197
It depends on the person how long you can stay up for WBTB. You should have a fresh mind but your body have to be tired enough to go to sleep again. I think six hours of sleep is not enough for WBTB. You have to sleep for 4,5 to 5 hours then stay up for 45 min. to 90 min. ( depends on the person ) and then go back to sleep. So you should get more sleep and a regular sleep cycle and talk to your brother .
I have the same problem. When I notice that it take a long time for me to fall back asleep I think about the things that I want to do in my LD or how it feels when I get lucid. That focus your mind that you want to become lucid.
Maybe it´s the wrong technique for you…Have you tried out MILD? Or start doing RC´s throughout the day so you can get a DILD.
In this Topic you can find some techniques: https://community.ld4all.com/t/all-ld-techniques/24932
Good Luck!