You’re right of course. L/D max would equate to maximum endurance, but max range (which is very close to LRC) would be faster.
Here’s a quote from NAVWEPS by HH Hurt:
“The maximum range is obtained at the aerodynamic condition which produces a maximum proportion between the square root of the lift coefficient (CL) and the drag coefficient (CD). In subsonic performance, this occurs at a particular value angle of attack and lift coefficient and is unaffected by weight or altitude (within compressibility limits).”
Unfortunately, he doesn’t mention the actual angle of attack. I could look further into that very good book but I’m a bit busy right now.....