Angle of climb at Vx and glide angle when "overweight": five questions

I did more brainstorming at work before going home early with a
headache...this is regarding the last point in my post.

Just to reiterate, I wanted to know why your best glide angle was
independent of weight whereas your maximum angle of climb was.

Here's what I came up with with a FBD:

For an aircraft climbing, unaccelerated, where theta is the flight
path angle.

T = D + W*sin(theta)
L = W*cos(theta)

For small theta, cos(theta) = 1 and sin(theta) = theta

so we now have

T = D + W*theta
L = W

flight path angle is given as (T - D)/W [Eq. 1]

or T/W - D/W or T/W - D/L or

theta = T/W - 1/(CL/CD) [Eq. 2]

First, you'll notice that the first term of Eq. 2 is the thrust to
weight ratio and the second is the lift to drag ratio. To increase
theta during a climb or minimize theta during a glide, one must
minimize the second term by flying at best L/D AOA. For a given
thrust, decreasing weight will increase theta.

The equation above would apply for both climbs and descents. What's
interesting to note is that in a glide when T = 0, Eq. 2 simplifies to
theta = - 1/(CL/CD), independent of airspeed or weight. The
dependence on load factor mathematically vanishes when the engine goes
out. How strange!

However, when flying with engine thrust and at the best (L/D) AOA, an
increase in load factor will IMPACT theta, lessening the climb angle
or making it more "negative".

Don't you find it coincidental that the absence of thrust makes the
dependence of load factor upon theta vanish? Can it only be explained
from the math?

So somehow, the magic equations seem to explain my confusion...but I
am not quite at peace. Au contraire. I've only talked about L/D,
weight, and thrust. What about drag? I am still claiming that you'll
experience an increase in drag with a weight increase REGARDLESS of
whether or not you have thrust. Thus, due to the increase in drag and
REGARDLESS of thrust or not, your angle THETA will be affected (i.e.
theta will get larger, more negative, airplane will pitch DOWN). In
the case of gliding flight, everybody but me agrees that your glide
angle won't be affected. Obviously, I am wrong but I don't know why.
To reiterate, that's why I've been writing all this stuff, 'cause I
don't get why THETA happens to change only when you have thrust but
doesn't when you don't have any and are gliding.

Alright, so the increase in drag with respect to load factor is shown
as:

D = V^2*CD where CD = (1 + CL^2)

By virtue of increasing your load factor (either via CL and/or V),
your drag goes up...[right?]

Now, try to tie that in to Eq. 2 in a desperate attempt to explain why
an increase in DRAG won't cause a increased glide angle (less range)
but will cause a logical decrease in climb angle.

From D = V^2 * (1 + CL^2) and theta = T/W - 1/(CL/CD)

Well, I'll stop here because I seemed to have taken the wrong path, as
I am pretty much stuck. ARRGHH! I AM GOING TO KILL A TURKEY!