Wow. I’m going to think about this one but, here are some thoughts that have come to mind. Not knowing your boat, I do hope that you have kept your old stanchion base plate for reference below decks for the new stanchion install. Are all three nuts embedded or, are the two inboard nuts accessible from the cabin? Is the outboard nut embedded in the hull? So, if the inboard nuts are accessible in the cabin then drop the two inboard bolts through the deck and fasten the base plate in the cabin snugly. This will give you the ability to locate and mark where the blind nut is. Hopefully it’s just in a place where you can’t comfortably access but, with effort someone smaller than you can reach. Now here’s the part where you have some options.:
1) You can attempt to use a “Speed Out” or other some such broken bolt/screw extractor. I would not skimp on the quality of the extractor as you are drilling into a hardened and brittle stainless steel bolt but, whether this works or not, is the question. If you have a cordless variable speed Dremel Tool, this will help you keep the extractor centered on the work surface. Patience will be the key. Hopefully this works as it’s the easiest solution (assuming your retaining nut is embedded).
2) If option 1 doesn’t do the trick, then you can get an appropriately sized wood plug cutter hole saw which you can use to “cut out” the material around the bolt and then with a hemostat or needle nose pliers you can coax what I am assuming is an embedded nut out of it’s hole. If this works, you can oversize drill and pot the hole, redrill and then embed a replacement retraining nut to remount the new stanchion. Now, if you were able to mark the location of the embedded nut from the cabin/underside and cannot nudge the embedded nut out, I would suggest that the easier approach is to drill out entirely and let the old retaining nut fall through to the bottom and then proceed with sealing the underside of the hole and preparing the retaining nut for the new stanchion. I use West Systems epoxy for everything on my boat and they have excellent manuals, specific instructions and videos for what I have suggested you do.
I hope this helps. I will look forward to seeing exactly how things look from in the cabin as you access what needs to be done to effect the repair.
George