The bottom is not completely flat but works fine with my stir plate.

The center raises from the edges. The center is flat for about 3 inch diameter. The rest has about 1/4” change from outside edge

Unfortunately you are correct. 1-gallon takes the level up to the bottom of the threads of the lid so you have maybe 1/2” of space above that . I have used it for wine only and some of the foam came out the tube I used that goes to a cup with some Star San. To fit the hole in the lid the tubing is pretty small like 1/4” ID. I think you will need to reduce the size of your batch by 10% or so to leave headspace to brew in this vessel. The Krausen from beer may plug the tube and make a glass bomb so be careful.

It has plenty of space- even my most aggressive batch reached the upper neck without coming through the airlock. I even bought a few others to split batches over and experiment

You are correct that there is very little headspace for krausen (foam) when doing a beer batch. As the other answer says other fermentations don't require as much headspace as they don't foam as much. If using this for beer we would recommend a nice blow-off tube or doing a slightly smaller batch to create more headspace. Perhaps you could brew a 1.5 gallon batch into 2 fermenters and try out your recipe with 2 different yeasts.

The gallon fermenters I purchased have been used for mead and melolel they have been great for experimenting with different recipes. Once perfected I'm making 5 and 10 gal batches. You are correct that the 1 gal fermenters leave little room for headspace which leads to blow off and a mess. Also with the space for yeast bed the yield is less than a gal. Cheers!!