Those curves only do lift related drag they don't do form drag.
Your assertion is wrong.
If those curve consider only the drag due to lift, i.e. the induced drag the L/D curve will be a monotonically decreasing hyperbola with infinite value at near zero AOA.
Lift induced drag coefficient Cdi ∝ Cl*Cl (Lift Coeff squared), hence lift by drag Cl/Cd ∝ 1/Cl.
My instant thought was that max rate of decent is when you have zero lift or even neg lift and max drag.
Zero lift and all drag is not a flying object (like kite, firsbee, airplane, glider), Zero lift and all drag is more like a falling stone, hail, rain, round parachute, such an object will fall ultimately with its terminal velocity.
Because you want as little lift as possible I discarded the variation of the lift related drag because you will be running at the very bottom of the curve and in the grand scope of things it will vary slightly but it will be under 5% in the grand scale of things.
This is where you are committing the fundamental mistake. It is true that for a descent lift required by an airplane is less than the lift required for cruise. But not near zero lift.
If the airplane were descending through a glide path of
ϑ,
the lift required to sustain weight W of the airplane will be
L=W*cos(ϑ) or W = L/cos(ϑ)
For a glide path of -3 degrees L = W*0.998, or just 0.2% less than cruise lift, descend doesn't take you to the bottom of the curve, a free fall may.
What if the airplane were climbing at 3 degree, we put three degrees again and find the
L = W*0.998
Surprise, even for climb we need less lift than level cruise.
Drag is energy removal you have zero (in know residual thrust but its going to be the same for any weight) so the max rate of decent is going to be a function of the energy removal of potential energy.
Drag is a means of energy removal, in fact when you multiply Drag by TAS, what you get is Force*Distance/Time = Power
Hence
D*TAS = Weight*(Descent Rate)
Energy Dissipated = Change in Potential Energy
D*TAS = [ L / cos(ϑ) ] * TAS*sin(ϑ)
TAS cancels out from each side,
D = L * tan(
ϑ)
or
D/L = tan(ϑ) = (ϑ) .... ( For small thetas)
This is how you write the energy conservation from an engineer's point of view.
D/L = Flight Path Angle ( expressed in radians)
or Flight Path Angle = 60* D/L ( Expressed in degrees)
I hope this helps... if you have nay doubt just post here...
But I like you thought process, it is somewhat akin to detective work.