Well, it turned out that the striker plates positions were the problem on both doors. They both needed to actually be moved out and not in!
It was the info from Bill about the latches having two closed positions that got me to thinking. Originally I could push the latch by hand to the first closed position. I couldn't move it to a second position by hand and therefore I was assuming there was only one closed position.
Now knowing about the two closed postions, I used pliers and was able move the latch to the second position. It's also obvious looking at the backside of the switch that there are two closed positions. The second position, however, is much stiffer to latch into than the first.
So now I realized that the strikers were too far in, and the door was running out of space against the cab when being closed. Therefore, the door was tight against the body before the latch could go into its second closed postion.
As for the weatherstripping, I did have it on backwards, as bartamos thought might be the problem. That wasn't causing the problem however because I was able to fix the door looseness while it was still on backwards. But I have since taken it off and put it on correctly. Now the doors fit snug and you have to slam them to get them to shut all the way as Bill said it would be. Also, the weatherstripping did come new as two pieces, but they were cut to fit.
Thanks for all your help guys! I hope to post some photos of the truck soon. FYI, this Apache is a driver and a work truck. It ranks high in character and patina.
James