As you already mentioned, the lathe came with an adapter sleeve originally. Mine too. And looking a specs in a brochure, it claims spindle taper as MT4 for mine, which is actually my tailstock taper. A 13" is listed as MT3. Again presuming both had adapters. And the adapters would give a matching taper to tailstock. I bring it up because I think you should measure the large end/opening of your spindle. Presume its a morse taper, and use your measurement determine if short/ stud mt5, or mt4.
I read the MT "short" taper in your original post but could not find it again. Thanks for linking. Mine is 1.7XX off the top of my head which would put it in the MT5 range. My issue is my through bore is only 1.312. The MT5 center hits the small end (1.475") after it clears a relief around 3 - 4" (likely cut to give dirt a place to go). Looks like the 16" models have a 1.562" bore which explains how you cleared the reamer.
I don't 100% have a reason to "fix" this outside of that I was going to run a reamer into the spindle to deburr the hole for the test bar. Now it's just kind of on my mind to "fix" it. I can't think of a reason extending the relief after the taper would hurt anything. If I go 5.25" from the face, most MT5 reamers, test bars, and centers should clear. So I think