There's Lois in Los Angeles, and there's Gemini in Chicago, and there's probably a local acrylic fabricator who might be able to do what you want. But the smart money is with the established makers, who are familiar with our framing needs. Generally, their work is better quality than the locals, who mostly do industrial work less visually demanding than for framing.
Instead of screwing the acrylic box to a strainer, I suggest you consider using a frame and using strips of acrylic, bonded outside the open edges of the box by your fabricator, to fit into the moulding's rabbet. This makes a much cleaner design, without the stresses of drilling & screwing the plastic.