I was able to get the body side moldings installed last night.
Here's how I got them straight, and right back in the production location, in case anyone cares:
I left the moldings on the pickup box in place up to this point on purpose, so that I could use them to guide the installation of the new moldings at the rear of the cab. I also marked the location at the front on the old wheel opening moldings. I temporarily re-installed the old wheel opening molding and ran a piece of tape between it and the rear...
I wiped the side down with rubbing alcohol and then installed the little piece on the front fender (which I warmed in the oven at a little less than 150 degrees for a few minutes to make it more pliable) and then installed the small piece on the cab corner.
The door molding is pretty floppy so I wanted to support it in the middle somehow. At first I thought I could use a 2x4 but there is quite a bit of "bow" in the door. I ended up using this small piece of angle aluminum, with some tape on the back side and a few notches cut so that it could bend slightly in the plan view. I nested it up underneath the two pieces of molding that I just installed, layed the door molding on it and pressed it against the door...
and VIOLA they are all in place. After pressing them on by hand I rolled them a few times using Momma's rolling pin from the kitchen (which I discreetly returned when done) and then installed the new wheel opening moldings.