There could be a couple of other culprits here. It could be something as simple as an out-of-balance wheel. Just for fun you could swap the rear wheels and tires to the front and see if the condition gets better or worse. Could be an out-of-round tire. A good set of radial tires does wonders for the steering and handling of these ol' rigs.
There is an adjustment procedure for the steering box. You'll need a cheap fish scale to do it. There should be very little free play in the box.
Here is the procedure. I run a steering stabilyzer on my '53 and it really seems to help. It's a Moog SSD12 available at any NAPA.
Hope this helps. Keep us posted.
