Just be aware that stainless is usually not the best material for this application. Shafts are made from Aquamet/Aqualoy or Nitronic which is substantially less prone to crevice and pitting corrosion than 304, 304L, 316 or 316L.Short version: boat hauled out last weekend. The stern tube/log was corroded and broke into bits when I tried to tap it out. Got the boat out of the water in the nick of time, I guess. So had to take off the shaft (easy just by taking off the strut) and I'm having a new stern tube fabricated out of stainless for $50. It just bolts on to the hull and the dripless packing hose clamps onto it. I'm going for the 5200, permanent fix. Gob the stuff all around it and over it and it should last for forty years. Pictures will follow next weekend when I put it on.
The bronze used for seacocks and stuffing boxes would be more appropriate and it is called 85-5-5-5 bronze or eighty five three-five.. I suspect your log was simple brass or manganese brass with a high zinc content if it fell apart like that. you may also have a DC leakage problem on-board your vessel. I have never seen that happen to an 85-5-5-5 bronze and I have worked on many bronze seacocks out there with 40+ years on them. I have seen a manganese bronze prop literally disintegrate & fail on the same boat that has 85-5-5-5 seacocks and the seacocks showed zero signs of problems.
The best solution would obviously be to glass in a fiberglass shaft log then no worries about corrosion. If you do use SS inspect it often for crevice corrosion as the shaft log is an area that is VERY prone to oxygen starvation. This is especially true if using a dripless shaft seal that is not vented or a drips-less packing.