Having worked quite a bit with plastics (years ago), I can offer you a few tips.
I'm not sure of the ringing problems, but know that cast acrylic is quite dense. I forget how dense lexan is.
But, yes, they are both quite flexible, being nowhere near as stiff as glass.
Both will scratch very easily. Matter of fact, they will scratch with just regular cleaning, never mind during the fabrications process.
Lexan is not UV stable, it will yellow, get foggy, and develop spider cracks over time.
Lexan is much easier to cut, you can cut it with a good, sharp blade designed for cutting melamine. Acrylic is much more difficult to cut it without chipping, or with the corners not breaking off as you reach the end of cuts. Acrylic requires a different blade.
If you manage to get chip free cuts, then you can sand the saw mark out, and use a torch to kiss the edges and flame burnish them to a shiny transparency. This requires practice to not distort the sharpness of the edges.
There is a glue for plastics that comes in a bottle with a syringe type needle for application, you fix two pieces together, and run the needle along the joint line, and they are permanently bonded. The fumes from the glue are quite hazardous.
Cheers