Don't attempt to switch the cages. The easier route would be to switch out that monster freewheel for a smaller one. I have several that should work.

According to VeloBase.com, the GA shortcage RD will shift to a 28t rear cog. I have a 26t and a 28t freewheel I can send you tomorrow.

Also, you are going to need a couple of ferrules for the top of the brake levers. The Shimano 600 brake levers require a special one (larger) if I remember correctly. I'll look into that for you.