What you're describing sounds like the transition from REM sleep to a shallower state. If this is toward the end of your sleep, there might be another REM period along in short order (it'll generally be somewhat longer earlier in the night) If you have any practice at WILD, you should be able to carry on from this half-way point of a WILD - i.e. *don't* stretch, just wait for the next REM cycle to start and you're in an LD!

On the other hand, it's difficult to muster the presence of mind for this :-P