flybubba,
In advance, this discussion relates entirely to the 'CAS' phase below the level where Mcrit is encountered, thus all statements here are relevant to low speed drag polars only.
What you say would be (almost) absolutely true if we descended at a constant EAS, but we don't, we descend at a constant CAS.
Weight during this phase is constant, if we ignore the very small weight reduction caused by the 15 minutes or so at idle thrust. (If we did consider the weight reduction due to the fuel used, Weight, and Lift required would be LESS). Thus, Weight, and Lift, are constant, because Lift = Weight. Drag, on the other hand is increasing due to increasing EAS at a constant CAS as we descend (6.3% increase in my earlier example). So, whilst Lift remains constant (actually reducing slightly), Drag is increasing, and the L/D ratio is definately not constant. As you have correctly indicated, glide angle is directly related to the L/D ratio, and a decreasing L/D ratio will result in a steepening glide angle. This steepening glide angle is mitigated to some degree by the translation of kinetic energy into 'effective thrust' as TAS reduces.
To sum up the 3 factors involved -
(1) Weight, and therefore Lift, reduce, leading to a lower L/D ratio, and steepening glide angle,
(2) Drag increases due tincreasing EAS, leading to a lower L/D ratio, and steepening glide angle,
(3) Kinetec energy dissipation due to deceleration (decreasing TAS) translates to an effective drag reduction, and a degree of abatement of the increasing glide angle.
Regards,
Old Smokey