Dead center fit?

One of my lathes if a Morse 4.5, and another is a Morse 5.5 Probably you have a Morse 5.5...
 
... I should add that you can fabricate a sleeve for your tailstock for inexpensive MT3 tooling...

Probably the sanest way to go...
 
Using the 2 indicator method I have determined that the taper is .059" per inch or .708" per foot! So maybe .060"/.720" if you assume I didn't get the indicator perfectly on centerline? Does that taper match anything?
 
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No idea what the taper is in the spindle, but the manual implies there is a bushing to insert and THEN a No 4 Morse center fits.
Like a South bend it is probably a proprietary taper.
 
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