Thanks for using Just Answer, from what you have described the most common cause of the problem in which you are having is a defective TFI (Thick Film Ignition) module, which is located on the distributor shaft. I am sending you diagram pointing out the location, hope this helps you out.
REMOVAL & INSTALLATION
WARNING Step 5 must be followed EXACTLY; failure to do so will result in damage to the distributor module connector pins.
Yes the distributor does not need to be removed.