For solvent bonding for items like boxes or any right angle construction, a laser cut edge isn’t 90 degrees from the face, and will present less contact surface area. A saw cut is better for a flush fit and strength of the joint.
Do you know if that acrylic is cast or extruded. The reason engraving on cast looks good is because leaves a frosted surface. But if you wanted something polished like this extruded might be better.
Hi. I love your project. 3D grayscale like those can be found on internet but I always prefer to understand how things works. Is it a complex process to do those type of images? With what kind of software have you done those?
The grid pattern I created in Adobe Photoshop and the spiral was something I found online and then modified for my needs. The same type thing could be created in many photo editing programs (GIMP is free) and even in vector programs like Illustrator or Inkscape (also free).
Just the same image I was using for the engrave. A solid image would be an interesting test. It might make a more consistent finish across the entire surface. I also like the torch idea that was mentioned earlier.