Before pulling the battery, turn on the headlights and activate the starter with the ignition OFF. Either you or someone stand in front of the car while this is going on and see if the headlights dim way down as the starter turns. A slight dimming is normal, but if the headlights do dim noticeably and the starter turns the engine over even slower, the battery probably is weak, as has been suggested. Other than problems with the starter itself, this condition could also be caused by a bad ground, although you stated you checked that. You have also verified that the cables are the correct thickness and not auto parts store thin 12-volt cables. With a 6-volt system, good grounds (ground strap and an auxiliary cable) and the correct gauge cables are absolutely essential, something that you might skimp by on using a 12-volt battery. A 6-volt system is less forgiving.
Follow "ModelA29's" suggestion for establishing a good ground to the frame and use an external star lock washer to dig into the crossmember metal. Even though the ground here may look good, the mating area on the crossmember must be shiny down to the metal. I've been fooled by an otherwise clean-looking ground here that affected the starter's operation. Re-check this area and make sure you have the correct braided heavy-duty ground strap and that it is not frayed or corroded from battery acid. Be especially critical where the woven strap enters the attaching end. Often the two are separating from age, battery acid or over-torquing the strap at an odd angle.
Although engine pans only peripherally assist in the electrical system's performance, it's one more area that Ford engineers designed to complete the electrical path throughout the car. I'm not saying a lack of engine pans will cause a starter to turn over slowly. I'm just adding that the engine pans were designed to assist in the overall charging health of a Model A.
Marshall