I think a mantra that says you'd wake up after 6 hours would be way more effective than saying at 6.00 AM. I bet it's easier for the body to recognise how long it's been asleep for, and when cycles end, than it is for it to recognise which time it is. Use a mantra which will wake you up after 4½ hours or 6. This is usually around the time your 3rd and 4th dream cycle has ended or is about to end and you're in REM.

Although you always wake up when they do, it's just a matter of remembering them, so the intent should be enough