I may be a bit late to this thread but thinning rims is not a hard job and probably best done in a lathe. The best way to thin the rims is from the case side. I have done this back when Uberti first come out with their '76 Winchester. They set the headspace to the original instead of modern brass. The best way I found to thin the rims was to make a plug to fit snugly in the case mouth with a center drill hole in it. Then chuck up a piece of stock and cut a recess to just fit the rim diameter and to a depth slightly less than the rim thickness you need. Hold the case to the recess with  a tail stock center and use a cut off blade or other tool to feed straight in and out to cut the rim to thickness. Takes longer to put a case in and out than to make the cut. It  helps a lot to have the cases sized to the necks are all the same diameter. 
Hope this helps and the pics make it easier to understand. 
Sam

Very nice pics. Yes I have a carrage stop on my lathe that I use. What I do to measure rim thickness is I took a piece of round aluminum longer than the cases, squared eacn end and drilled a hole through that just fits the case. I then use a dial indicator on top of a flat disk on top of the case head to measure the thickness. The disk keeps your indicator tip from dropping into the headstamps.