Actually, I think Tinbasher and Jimi may have the basis of a solution to this one - silver solder and frozen peas. Here's how.
Make a new tang/bolster piece, with the tang and bolster a close copy of a proper Sheffield gouge. Something like EN8 machinery steel might be better for this than plain mild steel, because it'll be a bit stronger in service - less inclined to bend. Don't use silver steel, or anything that'll harden when heated. On the blade end of the new piece, make it about an inch long after the bolster, and cut a sort of 'bird's mouth' in it, in such a way that it'll embrace the maker's stamp on the blade, but not cut it. That'll also increase the joint area, giving the silver solder a better chance than a plain butt joint would have of lasting. Then carefully grind the remaining tang so that it fits into the 'birds mouth'. Silver solder needs a joint gap of about 0.005" at the most, so a nice fit would be needed. Care, patience and diamond needle files might be in order.
To make the joint, use a low-melt silver solder like Easy-Flo No.2 or Silverflo 55, and Easyflo flux. Clean the joint surfaces THOROUGHLY - absolutely clinically clean, no oxide films or finger marks (a really good rub with wire wool is good for this). Set the two pieces up with careful support to prevent them moving during soldering, and see that they're in line both side-on and front-on. Pack lots of frozen peas around the cutting-edge end of the blade - you don't want this bit to reach tempering temperature, less than 100C for preference. Use a heat source that concentrates the flame on the business area; a welding torch with a soft flame might be best, but failing that, a Sievert torch with a small nozzle. Flux thoroughly, and assemble the bits. Heat up and make the joint, using as little heat as possible. Then allow the whole lot to cool down as slowly as possible - DO NOT QUENCH. You want the tang end of the chisel to anneal, not harden. When it's all cool, trim up the joint with files and emery cloth.
It might be a good plan to do a couple of dummy runs with bits of scrap mild steel to get the bird's mouth about right, and make sure the blade end stays cool during the operation.
Sounds complicated, but it might work, and would give a strong, lasting joint if it did. It would also be far more controllable heat treatment wise than welding.
