Skelly,
The reason I tried the DIY containers was because Cliff England sent me several pounds of persimmon seeds one year when I ordered a quarter pound. It was late in the year and he was done seeding. I started mine in mesh flats that were only about an inch and a half deep. I lined them with one layer of wet newspaper. I put about an inch of medium in the flat and then put the seeds in. I covered them with about 1/4" of medium. As soon as they germinate, they try to pickup the seed and form a little loop. As soon as I saw a loop, I pulled it out of the flat and planted it in an 18 and then DIY containers when I ran out. It worked very well.
However, I was pretty inexperienced back then and made the mistake of planting hundreds of persimmon from 18s in the field. I don't think any survived and if they did, none flourished. Fortunately I did transplant some into larger containers and grafted them the next year. Those trees did well.
So, 1/4" is sufficient for germination. I'm guessing the large difference in depth recommendations is due to soil type. In light soils you can probably plant them deeper, but they may have an issue lifting the seed up out of the soil if it is heavier and more compact when planted deep.
Thanks,
Jack