Very little if any room. I have removed races like this from a round baler by taking a dremel and putting slits in it and then breaking, but the case probably could not take the beating.Heat gun or torch, anyway to push from back side?
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Almost what I did as I have removed several from round balers like I did this one in the pic and put a new bearing in and they were good as new.If you do not like the above suggestions take something like a dremmel tool with a cutting disc on it and thin down the bearing outer race as much as you dare. Take a small oxy acetylene flame and heat the thinned area until it turns color, now you can be sure what is the race, thin it some more, heat it with a small flame at the thin part to red. The bearing now will have a smaller diameter. One could just say take the mig welder and weld a half inch or so around the race, that would do the same thing but would put lots of expansion stresses on the case.