As I said, I was trying to keep the drawing simple, but I'm happy to provide more details.
First: The quill shaft is held in place by a large nut with a left hand thread (not shown) on the right side of the shaft. The length of the shaft between the bearings is about 0.015" longer than the space between the bearings. This slight clearance keeps both the quill shaft and bearings axially located without side loading the ball races.
Next: Oilite has been around for a very, very long time. It's a trade name of course for sintered bronze impregnated with oil...very easy to machine and properly lubricated will last a very, very long time. There is only minor stress on the pedal shaft and in this case, the bushings are about 1.5" long providing plenty of support.
On the 'real thing' the left pedal and pedal sprocket are mounted very near the quill shaft...this fixes the pedal shaft axially.
If this doesn't clear things up for you, let me know...I can always take a few more pics.