Almost all of my LD are near normal wake up time with most of them after it while sleeping in (and additional napping).
Also almost all of them are on weekends (when stress is low and sleeping in is possible)

But I don't just WBTB a little I sometimes practice sleep disruption (set an alarm to go off every hour on the hour to get me in the habit of waking often), I drink lots of water and I often use 5-HTP to both shift REM and to cause me to wake up in the night (makes brain more active latter in night). Usually I wake up at least every 2hrs more often every 1.5 most of the night and sometimes after only 30-40 minutes when napping. So about 3-8 times depending on the night.

Occasionally I will have LD that are at strange times like midnight, they are rare but it does happen. Also some LD I have forgotten and when I am journaling and thinking backwards thru the dream segments (after some random awakening time), and during the process I will suddenly remember a false awakening with false journaling, where I am recalling a dream segment in which I am supposedly journaling an LD from an earlier portion. Of course I then recall the lost LD.

So yes, I have some LD that are forgotten and recalled from the middle of the night, and some that occur at around midnite (likely due to supplements)