Adding a "bog" may help, but with this many fish, it would need to be of considerable size to fulfill your needs.
Why would you have a problem re-homing some of your fish? Others in your area may be quite happy to have them.
I live in a fairly rural area and I don't know anyone else with a pond in need of any decorative fish. Plus I'm attached to them! They're pets as much as my dogs and cats are. If I can improve filtration and keep them happy and healthy where they are, I'd much rather do that.
The bog size I have in mind is a 6' diameter stock tank with a 2' depth... Just eyeballing it next to the pond, it looks almost as big as the pond itself. I calculated the surface area of that bog to be about 28', which is more than 30% of the surface area of the 9'x9' fish pond. From everything I've been reading, I thought that would be sufficient for a filter system? The barrel system I have has worked 'til now but it's ugly as mud, and I've been trying to beautify my (sadly neglected) pond area this year and had planned on building some kind of screen for it. The bog would be a much more attractive solution, even if it takes up more space in the long run.