I don't know how to do this. Is there any way that I can use a mantra or something to "train" myself to fully wake up after every REM cycle?
It's all about intention and motivation. If you want to wake up after every rem phase badly, you will. I naturally wake up after 4,5 hours of sleep every day and I need to use will power to stand up and doing my induction techniques. In the time of increased motivation, I do dream recall and typing dreams every rem phase. I don't recommend you to use alarm, it can hit deep sleep phase and your upcoming day is ruined.