I set the toe in on my model A at 1/16 plus or minus 1/32. Improper toe in is usually what sets up shimmy and anything loose about the front end and steering will contribute. If the air pressure is low in the back tires this can cause shimmy. If the front spring is worn and sagged (usually on the drivers side) This can cause shimmy.
You mention adjusting the steering. You need to jack the front wheels off the ground. Tighten the sector thrust screw and slightly back off. Turn the steering all the way both ways and check for bind. If it binds you may have to back off more. The next adjustment is for worm gear end play. While sitting in the drivers seat, grasp the steering wheel and push foward and then pull back. If any movement foward or backward is felt, you will need to remove shims at the end of the steering shaft. To remove shims you will need to remove the light switch and spider. You will then need to remove the four bolts at the bottom of the column, I think they have 7/16 heads. After the four bolts are removed the end of the steering housing will slip right off. You should find a stack of metal shims between the steering column and the end housing, like gaskets. Removal of shims will reduce end play, it will be trial and error untill you remove enough shims. The object is to remove as many shims as possible without creating bind. with the front wheels still off the ground, turn the steering wheel from one end to the other and if bind is detected you will need to add a shim or two to relieve the bind. After these adjustments are made let the wheels back down for the next test. Watch the square sector shaft where it enters the pitman arm. Have someone move the steering wheel slightly from one end of the free play to the other. If the slightest movement is detected between the sector shaft inside the square opening in the pitman arm, you will need to remove the cotter pin and tighten the hell out of the pitman arm bolt. The slightest fraction of movement between the sector and pitman arm will end up as inches of slack at the steering wheel. Try it you may be surprised at the improvement.