How Do I Get The Damn Bearing Race Out?

I have a Syil X4 mill - about 10 years old. The spindle bearings are dead. I have successfully removed the spindle cartridge from the cast head housing. I have successfully removed the spindle from the sleeve that holds the bearings. I have successfully pressed out both inner bearings. I have gotten the lower, larger bearing race out. But there was a "gap" below that race to get my puller jaws into. The upper race has no such gap - there's nothing to grab to pull on.

I saw one YouTube...

How Do I Get The Damn Bearing Race Out?