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It should be possible to do some refinement of tolerances through repetition.
Lets say we use John´s tapemeasure* on the perifery metod to make a 2880mm circumference 1440 tooth marine plywood** hirth indexer (basically a pair of crown wheels with 60 degree teeth interlocking).

this should then be used to make a second set, If no great preassures are involved this second set should be about as good as most plastic sextants***, good enough? this could then be used to engrave the main scale.

What is to come is bit more daunting, the verniere, it will need bit more work as each line need a slight offsetfrom the perfect 1440 div, I thought of making a second set of hirth couplings, but then it dawned on me, I only need to move everything 1 extra line in 121 lines, that means I can likely get away with micrometer adjustment, it needs to move the arm holding the engraving tool mere 2mm ofset along periphery.

*Most 5m tapemeasures are within 1,4mm/m accurate and top class 1 witin 0.6mm/m over whole length so with a 2880 mm perifery accuray is better than 0.9mm along perifery between any two teeth (~1/4 tooth) and adjacent teeth much better than that.

**ok plywood flexes but lets make it say two layers 20mm glued screwed togeter for base with the donut we cut teeth into another 20mm, 60mm marine ply, pretty stiff and as whole donut is holding with all of its 1440 teeth...

***Metal hirth indexers are capable of fractions of arcsecond accuracy and ball indexers on same principle are even better.
Main reason for accuracy is that any errors are, more or less, averaged out.
This is also one of very few measuring devises that get better accuracy for wear (to a point).
Care to guess what is used to index the wormgear of modern drum sextants.