ube--I was thinking about how to do the seams since you have the same block side by side on all sides. The logical choice would be to press towards the background fabric in each of the 3 rows and the seams would nest nicely together. However, the seams will be going the same direction with the other blocks as well so when joining the rows the seams won't nest. I notice in your original post you mention your seams going all directions. I can see why.
I've just experimented a little on my last quilt with pressing seams open and that worked pretty well. I just kept the pins in and sewed over the seams very slowly and carefully. Maybe that is the solution. The other way would be to make half the blocks pressing one direction and press the other half of the blocks the other direction. This would limit how much you could move around the blocks when you are doing a final placement though.