I think that (if documenting it) you should keep as many accurate significant figures as possible, and let whomever is using the data determine what to discard or round to. The accuracy of your caliper or mic would determine this. Say you have calipers that are only accurate to 0.01", then the part measured as 1.505", should be documented as 1.51". But if your tool is accurate to 0.001", then document 1.505".
The point of 'accuracy of construction' is valid and needs to be taken into consideration. If this value is unknown (most likely), then you should not assume or guess what it might have been and rather document it as "measured to be 1.505" not "the original part was 1.505".
Another consideration is wear of the part. Some materials will wear over time and this needs to also be taken into account. Probably doesn't apply here, but I do not know what the DOT spinner is made of... In that case you could document it as "measured used part to be 1.505".
I don't think that you can assume that since 3.63" is close to 3 5/8", that (while most likely) "the engineer intended it to be 3 5/8". Who knows what the engineer was thinking? Perhaps he moved them until they felt/looked right and 3.63" is what it happened to be. Or maybe his birthday is march 1963 - OK that may be a stretch but the point is that you don't know so you can't assume.
Yeah, this is all pretty anal on my part, but without knowing the use of the data, then I say keep as much accurate data as possible. I guess when you said "documenting", I think of accurate data to be used by unknown people for unknown reasons. Now if you were simply "documenting" for your own use to build a CP, then there is nothing wrong with calling it 1 1/2" and 3 5/8"....
Rick