A good way to figure out your normal REM times is to use your natural midnight awakenings. Your body will naturally wake up after each REM period. Make a point of waking up more fully than normal, and jotting down the time each time this happens. If you do this for a few nights, you should see a pattern.

Your REM will shift around, but you can at least get a feel for what your mind is doing. For example, I try to go to sleep around 11:30. I know I wake up from a dream every night around 3:00am. I also have a REM period around 4:30, and around 6:00 or 6:15.

The problem is, if I set an alarm for 4:00am to catch myself in a dream, it will work for a day or two, but then my REM period will shift to accomodate this awakening. Your brain is very slippery.