Have you ever tried morning naps? Maybe 1-3 hours after you wake up in the morning? Naps are a prime time for lucids. I get ALL of my WILDs and 95% of DEILDs during naps.

Sometimes I wake up at normal waking time, have breakfast, check emails, get dressed, then watch TV in half-reclined position on sofa. When sleepy, turn TV off and WILD.
And sometimes I wake up before my normal time, do the same thing and WILD.

Maybe your medicine will wear off by morning. Good luck.