A little unconventional, but I see your dilemma. Your pond is at the high point in the system.
If it's functioning well as is, why change it?
There are so many bog builds that have broken the so-called rules and they work just fine.
The goal is filtering the water and if your original design is accomplishing that, why not leave it?
Here's what I see, for what it's worth...
In your first drawing, water is being skimmed off the surface of the pond, not being pumped from the middle or near the bottom. So, basically you have created a big skimmer.
That might be what you want, I don't know.
Maybe if the water entering the pond has enough volume to stir things up, it might help.
In your upgraded version, what is the purpose of the perforated pipe? It looks like it's just sitting there doing nothing, unless I'm missing something or I'm misinterpreting the drawing.
You are pumping the water into the bottom void and it flows up from there.
How will you create that void? Some sort of shelf to support the gravel?
Most of us pump the water from near the bottom of the pond to the bog. Then through the perforated pipe and it rises up through the gravel. No void.
Some people use a snorkel and centipede instead of the perforated pipe.
I'd leave it if your water is clear, unless you are having other problems.