I'm not sure how well this will work, but I'll go ahead and suggest it anyway..


What I would suggest is setting music up to play during the last 5 minutes of Your REM Periods, I mean, set alarms with music as the tone for the alarm (I recommend classical music.) and then set the alarms for 5 minutes before each REM Period ends, in theory you should hear some sort of form of the music play in your dream when it goes off, just make sure it's not so loud that it will wake you.

If you're unsure of how REM Periods work and there timing see below.
Spoiler for REM Periods: