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Yet another way is to use an edge finder on each side, and move to split the difference. A wobbler type edge finder is pretty cheap to buy.
As for a scriber that is on ctr height. Turn a point on your scriber, don't grind it. Then mount a piece of bar in the toolpost and a ctr or spot drill in your chuck and drill the bar followed by a drill of the scribers diameter through the bar which will put the scriber point on ctr height whenever you fit it to the toolpost.
I must endorse Chris' advice to use the mill to directly determine the midline.I long ago decided that marking out had its uses but for the most accuracy using the tool that will ultimately make the cut is far more accurate. To that end I fitted both the x and y axes of my mill with two inch dial indicators. Each indicator is fitted with an adjustable "striker" that allows the indicators to be used regardless of the mill table position.Once I have the mill table in its working position I set each indicator to read one inch. This allows me to accurately measure one inch in either direction with the accuracy of the indicator, nominally one thousandth.If you must mark out, one possibility is to mount the rod horizontally in a V-block/machinist vise/etc. so the face to be marked is fully exposed. Then set a height gauge to the appropriate height and, with everything sitting on a surface plate, scribe the line.
Nice, that's turned out well, following along
Hi PaulLooks good, I like the 'block' appearance, what's coming next ?Andrew