Now that I TYPE that, I was able to find this manual https://www.sterlingmachinery.com/media/brochures1/file/procunier-tapping-and-drilling-brochure.pdfI'd wonder if at least you could get a shorter R8/MT3 adapter. The image here looks way shorter than yours which might buy ~3 inches back: https://www.amazon.com/Shank-Drill-Chuck-Adapter-Sleeve/dp/B07NYN26DX
I couldn't find sufficient documentation on this one to see if it is replacable, but a handful of the ones I looked at were actually JT33 with an adapter.
It DOES look like the arbor is screwed in, however the exploded view does make it seem like it would be easy enough to turn a replacement in a straight shaft.