Can you find a piece of 1 1/2" or 2" bar stock for the CHINS bar? Alternatively, maybe you could cut a couple 10-12" lengths of 2" steel pipe and slide them over the CHINS bar before you weld it onto the cage. Might be cool -- kind of like the Rolling Thunder of CHINS. Then, you could just slide the pipe out of the way when you want to do CHINS w/ the skinny bar. Kind of like this...
