How old are the tires. When slicks get old the sidewalls breakdown and affect the handling. I would look for a set of drag radials. Do NOT put the biggest tire you can fit on your car. Bigger tires add more rotational weight and more drag. The result will be you will go even slower.
On my 67 Dart a 255 radial fits nicely with the correct offset wheel. In reality the car would be .1 seconds faster with a 235 due to the reduced rotational weight.