To transition from Code 83 to Code 100 is very simple - provided you know a little trick of the trade. Before you install your rail joiner, take an Atlas snap saw, or other metal cutting saw. Halfway along the rail joiner, cut the two sides that are folded up (these are the sides that will slide along the side of the two rails). Make sure you don't cut the bottom metal strip!
Slide a pair of these modified rail joiners onto both pieces of rail (or switch). The Code 83 rail will be 0.0017" below the top of the Code 100 rail (0.0100 - 0.0083 = 0.0017) (I've probably got the decimal point in the wrong place.)
Slide a piece of shim (a file, some styrene, a tie, etc) under the Code 83 rail. Gently press down on the Code 100 rail until the top of the Code 100 and Code 83 rails are level with each other. Solder the rail joiner and rail.
Bob M.
PS - If you use Atlas or Peco rail joiners, you will find that they are quite long. Simply cut off about 1/3rd of the rail joiner with your snap saw. Slide a piece of rail into the rail joiner and file off any rough edges.