Sean, is there a plate with nuts/bolts to connect the two arms, and then in the middle of that, a hole into which you attach a slide hammer?
Before I bought my Pit Posse bearing and seal driver set, I'd do as you mentioned, use the old one to drive the new one. I also use a deep impact socket laid across the bearing, and then gently tapping on the center of the deep impact socket, until the outer shell started into its hole evenly. Sometimes you get it right-away, sometimes you have to repeatedly reposition the bearing and the deep impact socket until it aligns properly, and the bearing evenly begins to seat.
I've also cut a slot through the outer bearing shell, which then provides some room for compression of its external diameter, as you use that to seat the replacement bearing. It's similar to Sean's reducing the outer bearing shell diameter with some sanding/grinding, to prevent it from itself being seated as it's being used as a driver.
I was long-ago taught, "never use force on the inner bearing shell!" This is referring to setting the replacement shell. Drive the outer shell. Being a backyard hobbyist, I don't do mechanical repairs for a living, so sometimes mentioning things like this may benefit someone.
Another thing to bear in mind, never use a torch or do welding to heat a wheel/tire with air in it! At the very-least, remove the valve core. One of my co-workers on fire-rescue was on a call where the tech made that mistake while he was welding a wheel on a dune buggy. It cost him his life. A simple, stupid mistake.
