Eug,
One method would be to turn a (I assume Morse Taper) shank to fit your spindle with the other end turned to be a close (i.e. +.0010/+.0005 inch or +0.02/+0.003 mm) slip-fit to your existing bore.
Another approach would be to make your own indicator. This would be a pair of (say) 1:10 levers that pivot on precision pins and bores in the case. The first lever would have a hammerhead shape that will "follow" your part. The second lever, driven off of the 10X tail of the first lever, becomes the indicator needle for your display. I believe that one of the people from the old Home Shop Machinist magazine (Rudy K..., if I remember correctly) wrote an article with a "how to" on this subject.
It has been nearly 50 years, but this was one of the tools I made as an apprentice machinist. I also made a nice maple box for it, but it was one of the tools that did not survive a (1974) house fire. At 1:10 to 1;10 lever ratios, it would resolve things into the .00025 inch range (though, I admit, my Last Word indicator supplanted it in very short order as my lives in my tool chest instrument). Now, mind you. the one I made pivoted on jewel bearings (one of the points of the exercise) and the one I remember running across a decade or so ago in Home Shop Machinist did not go to that level of detail, but the article brought back warm fuzzy's of my hours spent finishing things off in the useful pursuit of skills & knowledge...
And, finally, there is always shelling out the lucre for an off-the-shelf indicator. .0005 inch resolution inexpensive ones run in the $20 range in my neck of the universe. Good and accurate ones still are fairly spendy (though, having had my set of indicators for more than four decades, I admit to being unaware of their current pricetag).
In terms of finding your datum for your pin & hole, my first question is, How will you make a tool follow your center and not the existing one? Otherwise, it is a case of finding a center and exploiting it. One method would use an indicator. Another would involve making a pair of concentric disks and using them to locate the centers of your new locations. There are others, but they are all variations on a theme from there.