You'll never get accuracy closer than about 1 degree, 1 knot, or a couple of significant digits of range, even if your instrumentation is dead on perfect. The way to introduce inaccuracy is not to skew the instruments but to force you do do more estimation. For example, don't mark every degree on that overlay, just every 5 degrees.
There's a similar situation with the bearing in the binoculars. There's no index line, so you can't estimate a bearing closer than about 5 degrees. The bearing scale in the binoculars is there for situational awareness, not to allow you to measure bearings. If you want to make it even less accurate, remove all markings except every 20 degrees. Your accuracy will still be about 5 degrees though.
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