.../...How do you get the left side carrier bearing race out of the left axle tube? There doesn't seem to be any way to get a hold.../...
There is a slight "lip"; i.e. the race has just a bit smaller diameter than the inner dia of the axle tube.
Make a circular metal plate, which has a diameter precisely matching the inner dia of the tube. Cut two parts off, each side. This leaves a "strip" with radius each end. Drill a hole in it, put a screw through. Insert this strip behind the "lip" and put a support to make the screw in the hole act as a puller, to remove the bearing race. Or if you can get in behind, you can knock the race out with the metal strip.
May be useful to put the old, worn race "in between", when you tap the new race in place (and as ggr writes, don't forget the shims!)
/Hans in Sweden
.