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I'm having trouble finding the right tire pressure. I ride a lot of soft sandy conditions and the bike seems to handle best with the tires almost flat. How low can I go?

I adjust my pressure depending on where I'm riding. I prefer to run them as low as safely possible.

My rule of thumb is.....ALWAYS run ultra heavy duty tubes and them air down till you think you can almost feel the rim as youi go over the hardest/sharpest stuff. Make sense? If you can feel the rim now and then, add a little more air. I carry a cheapo hand sized bicycle air pump from a sporting goods store. Small, light and everyone is always wanting to use it.

I guess the lowest I ever run (this is for where I ride) is 9-10 in front and 6-8 in the rear

We have some really deep, soft sand here in N. Florida. I was ALWAYS falling down in the sand. Someone told me to let the air out of my tires until I could "mash it with 'yer fingers". I felt the same way as you. They seemed to be almost flat. I spend the rest of the day with the rubber side down, so to speak. I was thrilled. When I got back to the trailer, I used my tire gauge to get a new base line. The front was about 8 or 9 psi and the rear just a bit more. Now I run them like that all the time. It made a big difference for me. The front end stopped washing out on me and I felt more confident to stay on the gas a bit more. That was the real issue. I was a bit shy with the throttle. As a point of reference, the sand here is unlike any I have seen anywhere. Similar to the stuff near White Sands, New Mexico. If you stop, the tire will literally sink down to the rim. Very fine and very deep. They call it Sugar Sand!

8 psi in the front - running a Dunlop Geomax MX51.
It does much better than the Dunlop D739 front at the same psi.

I lived in Charleston, SC for 8 years and know what your riding and the conditions.

I would go with a soft-intermediate tire there, or soft-mud tire.