I didn't go through all your math, but consider this:

Your engine makes the same power regardless of weight, so the higher
the weight the slower the climb.

However, as you get heavier you have stored more energy by climbing
(that's one reason why it took you longer with the same engine power).
With more weight, you have more stored energy per 100 feet. At a
higher airspeed you are also descending faster.

As you lower a weight you are releasing energy, the rate at which this
is released is effectively power (this is what maintains your airspeed
without the engine.) So your heavier weight and higher rate of descent
gives you more "power" in your glide.