Using the right thickness HDPE board say 1/2“ thick it could be done successfully. But if I were to try it I wouldn’t do the whole dash I would just do a pocket the size of the plotter and only angle it. Run the edges of the pieces on your router to round them and soften the look. Put your stainless screws in from side, again just so it doesn’t look so robust. Using 1/2” would allow you enough meat in order to screw the system from the back side of the dash it would hold plenty.
I would give it a try, I’m not sure where your at but most building centre's now days carry HDPE in a variety of colours and many now sell half sheets as well which helps in the cost.