Installing new door post wood should make a big difference in the fit of the door.You will have to test fit the door as well.Sometimes the door has a twist in it as well,specially if the door wood is in less than perfect condition.If twisted,the door can often be straightened by installing a turn buckle with a strong wire on the diagonal behind the door panel.The problem you are having is the main reason I have a 31 S/W sedan.I admire anyone that can resurrect an earlier 4-door as wood working is something Im not that good at.
I am not sure how the Murray door is made, but I had to replace all wood in my Briggs including the doors. The doors are far more difficult than anything else. My completed doors are not quite as perfect as I would like them, but pay attention to other fordors/TS and note that none of them are (at least that is what I have observed). Mine have a slightly larger gap (1/4") at the bottom than at the top.I broke down and bought one wood part from a vendor, and it didn't fit as well as the one that I had made, so I used mine. My point is that you should expect to do some modifying of the door part when you get it. Good luck!