Death wobble

Got any pics of the front end? It would probably make things easier for us to diagnose.
Generally a street driven straight axle car would run anywhere from 6* to 9* of positive caster without issue, a track only car can get away with more positive caster, more caster is more stable at high speeds it helps make the front wheels track straight ahead.
You can check your caster angle by putting an angle finer or digital level on the steering knuckle right above the king pin, it should be at least 6*
A steering stabilizer would help in your situation especially is the front tires are coming off the ground on launch.
How is the steering box linked to the axle? More importantly what kind of angles are involved? If the tie rod going from the steering box to the axle isn't parallel (or close to it) to the axle your going to have bump steer issues which can also cause death wobble.

Did the tie rod tubes also come from speedway?

When I put a straight axle in my 46 Plymouth using speedway stuff I noticed the tie rod tube seemed very thin and flimsy and would flex pretty easily. Luckily I haven't had any death wobble issues with mine but I did have some bump steer because of too much angle from the steering box to the axle.