Inelegant? Not really, a better term is 'functional'.
Especially when compared to fancy boogers sold by all the supply houses, attracting the gotta-have-it crowd as a conversation piece. This one-ups most center line gauges by representing both upper and lower planes.
I'll re-recommend finding centerline accurately, procedure that works if decent flat surfaces occupy the carriage.
Chuck and dial in or turn round stock of stout diameter, measure resulting size, divide that in half and record.
With height gauge, or depth mic and 1-2-3 blocks, 4-way caliper; find height from flat datum(s).
Subtract the half diameter from height just measured.
Centerline found!

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