The starter on a 1954 early Special with hydramatic should be a Delco-Remy 1107126. If this is the type with a large solenoid on the top, a sticky solenoid is the likely culprit. Unfortunately, I don't have a car or photo to look at, likely you do. It's likely you cleaned and lubed the solenoid too, but just in case it was overlooked, I'm posting the suggestion. I just checked the Delco-Remy starter section of 1955 Issue of "Motors" and it says "If the starter tries to engage (or remains engaged) when the engine is running, look for trouble in the dash switch or its terminals. They may be vibrating into contact with each other. This trouble may also be attibuted to a weak or broken return spring or hinge on the solenoid relay armature."