Changing to tapered rollers is a good engineering solution, but a huge job. Tapered roller bearings are much bigger, so you need carriers top and bottom, which means you need a longer stem etc and so forth.
As you have discovered, the original races aren't supreme of quality. However, being what they are, they are hard right through, and this is good. It means that you can re-grind them to clean up the bearing track fairly easily. The four races will all be slightly different ID. Measure them, then make a tap-fit arbour to suit the largest. Using a die grinder or a Dremel with a 3/16" mounted stone, while running the race in the lathe in back gear, it's a matter of a few minutes to produce a lovely new surface. Knock that race off, take a whisker off the arbor to suit the next largest ID race, and repeat.
Getting the races off and out is gorilla work. To get it off the bottom yoke, start with a small cold chisel, working gently one side and then the other until it is far enough off the yoke to get a better drift behind it, although it won't have to come far to be onto the clearance diameter and free. Knock them out of the steering head with a long bit of rod held against the opposite side of the other end to keep it on target. Again, work it from either side and it will come.
cheers,
JFerg