It would be interesting to know which flat screen monitors had a rigid, thick enough plastic for a router baseplate? I've dismantled several as well as a couple of large LED tvs and nice materials but thin and flexible (still useful just haven't decided for what yet.
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6mm clear or translucent acrylic is my first choice with polycarbonate a close second but I'm lucky as I managed a couple of plastic didtributors in my distant past and still have scrap.
What I suggest you do is some research of your local area, there may well be an Amari Plastics or similar distributor near you and they will have offcuts and scrap available. Look for Sheet or semi finished plastics distributors, also worth checking out, signmakers, thermoplastic form companies and asking in the big sheds for old display or counter screens. Shop fitters are another source as they scrap old screens from banks and shops and another source can be your local authority as they scrap / replace the polycarbonate in old bus shelters and it goes in the skip. A bit of lateral thinking and keeping your eyes open will get you what you want cheap or even free.