I am the author of this thread. I have worked as a chemist off and on since 1973 when I wasn't working as a geologist, teaching chemistry and math at college, or running a machine shop.
Interesting article from OSHA about processing car batteries, but I do NOT find it odd that they don't mention anything about stibine and arsine, since the specific processes they talk about do not put the battery recovery operators in any kind of position with the battery components where they will contact stibine and arsine gases. The work is done by commercial OSHA-approved processing methods out of contact with the batteries and the recovery and smelting are done with OSHA-approved commercial equipment and furnaces where the operators are quite deliberately not exposed to the debris and exhaust flue gases generated. The exhaust gases go through a long enough heating process where the stibine and arsine gases are converted back to the respective elemental form, as in the Marsh Test, that eventually become the oxides of antimony and arsenic, again quite poisonous but not quite as deadly as the gases they originated from.
You obviously spent quite some time researching the battery problem, but you are not understanding what takes place for the generation of stibine and arsine gases in a HOME SMELTING operation. First, the stibine and arsine gases are not generated in DANGEROUS AMOUNTS within a battery when sitting there or it is in use (they indeed are generated but at levels not considered hazardous except after years of daily exposure to extremely large multi-ton size batteries indoors) or being physically dismantled, the poisonous gases are generated only when the lead dioxide is reduced back to lead metal and when the calcium, antimony, and/or arsenic-containing lead mounting plates and hardware ARE MELTED DOWN. That is what releases the calcium metal and antimony IN A REACTIVE STATE into contact with sulfuric acid residues entrained in the lead dioxide/lead sulfate matrix of the battery plates. This small amount of entrained sulfuric acid cannot be washed out since it is both chemically and mechanically trapped in place until the lead backing plates are melted. When melted, the conditions needed for the MARSH REACTION are created, specifically the contact of antimony and arsenic with calcium metal, calcium hydride, and sulfuric acid with hydrogen gas generated from it in contact with the calcium metal liberated by melting, which all in concert generate the stibine and/or arsine gases. As far as generating sulfur dioxide and sulfur trioxide, the home smelting of batteries does not usually get hot enough to decompose the lead sulfate into lead metal and oxide, releasing the noxious and extremely irritating oxides of sulfur.
Yes, smelting car batteries at home can be quite dangerous.