What if I try a DEILD right at the end of an REM period?

Can I drop directly into the next one?

If you attempt the DEILD after several hours' sleep, then yes, you have a good chance of going right back into REM, as REM stages are very close together after 5 or 6 hours of sleep. Also, keep in mind that your brain's schedule isn't set in stone: if you're coming off an excellent LD (or even NLD) and you'd really like to head back in for some more REM dreaming, your brain will likely cut you some slack and get you right back into REM.