I'm getting in over my head here. Because I'm not familiar with the bearing race you need to remove,it's size or how it's situated in it's seat. But for what it's worth Harbor Freight has an inner bearing race removing tool for about $13** you might want to check out...with 3 clawed arms that adjust out from 3/4" to over 2" inside diam. And it's frame width is even more adjustable.
It would'nt work on my steering neck bearing races. Because they just set too flush in their seats for the H.F. tool's claws to catch on the edge of them. But if there's enough "lip" exposed on your race to catch on, I'd expect it to work pretty well.
No guarantee

just tossing an inexpensive idea at you.