To be completely honest, solving this puzzle was mostly trial and error for me. I initially focused on the top left corner and throughout the entirety of the solution path I focused primarily on testing how the diagonal relationships impacted the surrounding areas.
The Top Row
I spent a fair amount of time here, initially focused on the top left corner with a setup involving:
However, as time passed, and I became more and more frustrated with it, I had a realization that I was focused on one way and needed to try something new. I started focusing on ways to create the first 4 in the top corner, ultimately settling on the following as I placed and erased blocks along the top to simulate placing the L and what the impact below it was:
Closing the Obvious
Certainly not obvious to everyone, but considering I had tried many solutions in the area by painting and erasing, I knew based on the top row that the diagonal connections would only support one configuration:
However, since I still had the right wall to solve, my suspicions of the lower left corner had to be validated by closing the right side.
The Right Side
Here, I started in the bottom right corner closing the right side with trial and error while taking into account the impact of the middle and left:
Solving the right side confirmed my suspicions of the lower left corner due to the obvious connections required in the center:
The rest was as simple as following the diagonal connections: