Stan, after you un-string it but before you move anything: You can measure how high the bridge is screwed out from the body on each end. You can make a diagram, even measure where each saddle is sitting along the length of the threaded rod adjuster, and which way the bridge is facing. The first time I did what you're about to do, it went fine until I put mine back on backwards !
Anyway the measurements would get you back playing again quicker than having to start from scratch . . . These bridges can look quite nasty on a used guitar, but the great thing about the brass parts is that they can be polished back to like-new. You can do this to the bridge and the adjustable nut, but generally not the tailpiece as these are almost always clear-coated. And DON'T use brass polish on gold-plated parts.
When they're this dirty, you just can't get them right with the strings in place.
Best of luck,
J o e y