If you want to try the heat solution, I'd suggest that you simply take the chuck off its backplate, then, heat the rim of the backplate with a ordinary propane torch. It may take a few minutes of heating to allow it to get hot enough in the center to expand.
Do not try to expand the backplate by heating only around the center of it. The outside rim will act like a vise, and this will not allow the center to expand in a direction that will give you clearance.
You should attempt to heat it as rapidly as possible, to maintain the highest differential in temperature between the spindle nose and the backplate. You could even help keep the spindle nose cool by putting a wet rag inside of it.
You are still going to have to "hit it" to break it loose, even with heat. You can improvise by bolting a piece of flat iron to the chuck backplate. Make it as long as possible, and use a 2 or 3 lb hammer, no use working hard
You will have to find a way to adequately lock the spindle up solid, how you would do this without a backgear, I don't know. You don't want to break any gear teeth, so maybe you can provide counterforce on the outboard end of the spindle with a pipe wrench, or something, at the moment of impact.