Research shows that meditation can replace sleep. Instead of trying to incorporate it into your normal day, you can try meditation instead of sleeping. Meditation increases short-term mental performance and reduces the need for sleep. Meditation and sleep are hypometabolic states, in which breathing and other bodily activities decrease.
Both release stress, but the rest provided by meditation is much deeper than the rest that comes from sleep. Therefore, deeper ingrained impressions, or samskaras, leave the system. Depending on the type of meditation you practice, practicing mindfulness before bed could significantly improve nighttime relaxation. The peace and sense of calm that habit brings can offer enormous benefits for achieving a deeper and deeper sleep.
Many meditation groups (from what I understand, especially Transcendental Meditation) DO say that they can go for extended periods or even permanently without sleep, but they have never demonstrated this in a scientific environment. Instead of feeling defeated and losing your routine, allow yourself to practice meditation throughout the day as needed. But what about the stories of the ancient yogi meditating in a cave or in a mountaintop monastery for days and weeks without sleep? How do you do it? While expert meditators are able to go so deep that sleep is no longer necessary, incredible skills are required to do so. On a final note, it was my belief and the belief of my teachers (probably a semi-myth in reality) that many ancient sages meditated instead of sleeping and would in fact go a long time without sleep.
Practice meditation every day, go to sleep at your normal bedtime, and let your circadian rhythms restore naturally. Personally, I don't think sleep is necessary, but your meditation should be well advanced to compensate for it. Instead of allowing these moments to grow and continue to cause stress, you may want to consider meditating throughout the day. Using breathing exercises as a form of meditation for sleep involves focusing on and regulating your breathing, and then eventually slowing them down, indicating to your mind that it's time to fall asleep.
Herbert Benson, a Harvard researcher and one of the first advocates of meditation research, mentions this a couple of times, most notably in Sleep vs. While sleep is meant to replenish your energy and help you heal, meditation is designed to cancel the stress that made you feel tired in the first place.