This reply is the closest thing to good advice in this thread.
The only thing that's going to get that out without cutting a slot is a tack weld. Which will likely burn the wood. Just cut a slot. You can find another aged carriage bolt to replace it.
It's the nut recessed? If not, you can use a splitter on it.
https://upload.wikimedia.org/wikipedia/commons/7/72/Mutternsprenger_0610.jpg