I've taken a lot of 40's apart and never saw primer under the hardtop sides of a truck I though had original paint. Yours might be the exception!
Yeah the door pins can be tight and hard to remove if they've been in place for a long time. Get rid of that small punch you have and get a bigger one. I use these punches to remove door pins, they're long enough so you can hold them at a slight angle to keep the head of the hammer a little further away from the side of the door when hitting. These are Starrett but I'm pretty sure Harbor Freight sells knockoffs. And this is Krolloil the best penetrant I've ever used. Get those doors off the truck is much cooler without them!