You can't just swap the ring and pinion, and put it back together like it came apart. The shims from side to side will be different in just about all gear changes to get the correct backlash, not to mention the pinion gear has to be set to the correct depth. The differential spacers will be off quite a bit when you're changing ratios. If you've never done this before, drop the axle and bring it to someone with some experience in doing this and let them finish it.
If you're bound and determined to do this, you're going to need to find a thinner shim (those case iron rings) on whichever side you need more clearance and get a shim kit to finish it off. You can order them from your Ford dealer, but you'll need to know about what shim width you need.