With the muck of lots of organic material adding cement is a drill in futility. I had some experience with soil cement in Vietnam. Trying to build roads or building pads was a challenge with the climatic wet conditions. The laterite clay had no bottom when it got wet but when mixed with cement and vibratory compacting it became pretty good low strength concrete. That then formed the base to build on. We built our road beds at least 2' above the expected surrounding water level during the monsoon rains. We eventually asphalt paved the road beds after correcting flaws in the build-up. The Vietnamese were left with HS 20 grade highways. Many are still used today. The following is an extraction from that experience modified for where you have no solid base. I have much added construction experience since then also.
If you water table is really only 2" down your first job is to get up out of the water. Looks like your garage floor is only a foot above grade so not much to ply with if there is no way you can install a drain system. Unfortunately, dumping large rock of any size in it just keeps sinking into the muck until you shove it down to the clay strata; then that muck comes up at you as it gets displaced by the rock. Any rock you use has to be crushed so it keys together. That is the best chance to get a layer in that will not keep sinking. I would start with 6" minus with no fines so as things dry up the water drains down fast. Then make the next layer 2" minus. When you get above the existing grade is the time to add the fabric as you are now above the water. Build up with 1 1/4" minus with crusher fines to within 4" of the slab top grade of the lowest structure. When things dry out in summer get a vibratory roller and go over the whole thing then build back up to the 4" below slabs. You should then weather another wet winter and spring. It won't be cheap but that is the price you pay for building on low ground. My Daddy always said "Son, always build on the high ground".
Ron
If he told you that, I would be leery about what else he tries to tell you.
To all: Brazoria county is south of Houston running all the way to the Gulf Coast. I know the north end of the county has problem soils and requires pilings/posts to build a house. I'm also aware of soils in central Texas that require the equivalent of 7 feet of excavation and replacing with more stable soil -or- use pilings, based on drill core samples and an engineering analysis. I am also aware that very few houses are built this way and opt for a concrete slab on grade. It was 10 years before an engineering firm had to be brought in to stabilize one corner of the house. The biggest problem the OP has is drainage and based on the pictures, that will be very hard to address. But, he's not doing a house. What he appears to be after is a place where he can put stuff so that it won't sink into the ground. Whatever he does is going to require some on-going maintenance/rework. Large stones and Geo-textiles should do it in his application, a concrete slab should spread the weight out the best and require the least maintenance.I don't really know what to be leery of. Please, nobody here take this personally, I appreciate the time everyone took to offer advice, but the suggestions in this thread range from "just put down some road fabric" to what amounts to a civil engineering project. I'm really lost, and feel inclined to listen to whoever is geographically closest to me and deals with my type of soil and is in "the industry." That being said, his suggestion does seem a bit weak to me as a layman.