You just have to fly at the minimum power required speed to make that happen, which is well below best range / best L/D ratio speed.
...which is also referred to as
stall speed! Continuing remembering your basic aerodynamics... An airplane will continue flying at some point below the power-off stall speed, but power must be increased to do so.
Since a glider has no internal power available, glider pilots make use of this principal when they fly at "minimum sink" speed while thermalling.
What I don't see is how, given that you accept L=w cos (descent angle), you can maintain that maximum lift happens anytime other than minimum descent angle.
The key is here:
However, the sine of the descent angle is defined as the vertical speed divided by the airspeed. If airspeed is decreased sufficiently, even a slight increase in descent angle will result in a lesser vertical speed.
Maximum lift represents minimum descent RATE, not ANGLE. The descent angle in the equation you cite is actually a result, not an input parameter. Maybe the equation would be better stated as
Descent angle = arccos (L/W)
The only thing I can think is that perhaps when you say maximum lift, you mean maximum lift coefficient.
That may well be... Aerodynamics equations always make my head hurt.
I'm thinking of the top of the hump in the curve that represents stall speed, so if that's a Cl vs airspeed (or AOA) instead of a Lift vs AOA curve, that's what I mean.