From the pictures, does it look like I can move the condenser in front of the core support without moving that other cooling unit?
I would not do try to move the condenser unless you run into some clearance problems with the new fan. It would be a lot of effort and I'm not sure that size condenser would fit in front.
I think you are on the right track with replacing the thermostat and fan. I would still check the timing to make sure it is advanced properly at idle. That can make a big difference.
Regarding moving the transmission cooler that is in front of the condenser. It may not have to be moved to solve your cooling issue but, anything you can do to increase airflow will keep you, and your bronco cooler. Your A/C and radiator will perform better if not blocked by the transmission cooler.