I've only managed a few WILDs, so I'm hardly an expert. The few times I have succeeded I did a WBT after waking naturally at about 4 am (I tend to wake after each sleep cycle). The problem is becasue of waking after a sleep cycle, the next period of REM is likely an hour away, I just have to be super patient. That also means it's not too good for sleep quality of course!
I just ended up meditating, concentrating on my breath, and observing the imgery that came and went. About an hour later I was able to get a brief lucid - not very efficient!

I suspect that a WBTB in the morning, but nearer to normal waking time, would be better.
I will try again and see how it goes.