Another data point:
for the 7 am JFK-LAX on a Wed this week, there were 10 BE seats left.
Didn't get added to the list automatically but had to call in, at t-4 was the only one on it.

At T-2 I was still #1 out of 2 (DM on a X fare)

and in the end the BE cabin was full, not sure if the GA just started automatically moving up other medallion members, but there were about 7 or so names with UP next to them on the screen at boarding.

For comparison when I looked at the 8 AM flight it was completely booked in BE the night before.