Well, I figured it out. I ended up making a bearing press tool. In case anyone else needs help with this, here's how I made it.
The threads on the axle are a M16x1.5. You'll need the following items:
1. Axle nut
2. 5" length of M16x1.5 threaded rod (purchased from belmetric.com)
3. M16x1.5 female-female adapter (
Purchased from Amazon)
4. 1-1/4" x 9" steel pipe w/threads
5. Pipe end cap (drill a hole in the center of the cap large enough for the threaded rod to fit through)
6. 1-1/4" washer
Next, thread the adapter onto the axle and thread the rod into the other end of the adapter. Slide the washer onto the axle, up against the bearing.
Thread the end cap onto the pipe, slide over the axle and the threaded rod through the hole in the end cap. Now screw on the axle nut and begin to tighten. Eventually the bearing will bottom out against the axle shoulder.