The part that is hanging up is the second stage of the door latch. It is the safety latch which is designed to keep the door from flying open if someone were to bump the inside door handle by accident. Your door handle isn't lifting it far enough to clear the striker.
If lifting doesn't do it, have a helper turn the handle, then you climb in the cab and employ swift and blinding violence with the soul of your good foot near the latch side of the door.
Like you said, you need to get the door off. The only thing you may damage would be the striker, but you probably will need to work on or replace it anyway. They take a serious beating over time.
Carl

Last edited by 52Carl; 01/11/2018 11:18 PM.

1952 5-window - return to "as built" condition | 1950 3100 with a 235 and a T-5 transmission