You did not say if you have all the original hardware but if so I have a couple suggestions. The original driver side (most wear) has some 68 years of slams on it. This hardware and the door latch will most likely need replacement. I sourced a NOS set from eBay and it now works as per design. If you want to just go the adjustment route and see if it will work this should help.
https://www.flickr.com/photos/advance-design_parts_co/albums/72157641244124604NOS latch.
https://www.flickr.com/photos/advance-design_parts_co/25279723473/in/album-72157631868452754/Reproduction latches are truly garbage and do not work, they will and do fail within one or two closures. Keep in mind that used latches will also be the same age as the one you have, they may or may not work as needed.
The cab side hardware can be shimmed but should be replaced as well.
https://www.flickr.com/photos/advance-design_parts_co/8129483247/in/album-72157631868452754/I found in ordering the cab side latch as a reproduction and comparing it with NOS to be almost a 1/4" off where the door latch went over it. Again the reproduction hardware can be a problem. The last thing to keep in mind is if you install new weatherstripping the door closure dynamic will change until it compresses and beds in. As far as opening, now you are in the truck you should be able to get a screwdriver into the mechanism, remove the door panel and trip the hardware from inside, look at the pictures and you can see where to pry it. Good Luck!
https://www.flickr.com/photos/advance-design_parts_co/12647393234/in/album-72157641244124604/
