Nice demo, Vierbit!
Hopefully Olo understands the offsetting part. I do this with Photoshop, which has a filter that does it, found at
Filter > Other > Offset (just input half of the image's pixel dims in the horizontal and vertical fields). Very fast.
Olo, what about transitions? All you've posted so far are solid tiles. How do you plan to handle transitioning from one surface type to another?
You may not be ready to jump into transitions but you'll benefit greatly from getting a grip on the following.
Here's some more square tiling theory for you. (the following tile examples use 32px X 32px tiles. It's best to keep your tile's dims to a binary number for video card optimization [2,4,8,16,32,64, etc])
The simple 16-Tile System. With only 16 base tiles, you can make any combination of terrain.
Vierbit gets into creating tile variations above. Variations aren't even a concern here with this, though very relevant with making nice random tiling solid tiles that obfuscate the grid. You can have as many variations as you want, but they're not necessary to make the 16-Tile System work. Check it out:

See what Blizzard did with this method for WarCraft II. Below I've taken a screencap and overlaid the "simplified" tiles illustrating where the transitions are. (ignore the grey stone walls, they use
a different tiling system than the rest)

And here are the simplified 16-tile master sets I made to create every bit of the simplified overlay in the above screencap:

An additional example of WC2's tiles being simplified:

Seam Points are an important feature of creating good transition tiles. They're simply a standard place in the edge of each transition tile where the visual transitions between tiles must meet in order for all tiles to link up correctly.
The yellow dots overlaid in the image below depict where the Seam Points are. Critically important is that they're all the exact same distance from the corner of the tile closest to where the visual transition is taking place . . . if that makes any sense. I know it's confusing at first, but I promise it's all very simple in reality.
BONUS TREES 1 -
BONUS TREES 2 -
BONUS TREES 3This is all my own research, so lemme know if anything is unclear. A lot more could be said, the images may not speak for themselves.