Kasich might be good, as would his fellow Ohioan, Rob Portman. But I forget which pundit made a good point saying Portman was OMB chief in the Bush admin. and anyone even remotely connected with Bush probably could not be considered. Pretty sad.
Portman was White House Liason to Congress, then U S Trade Representative and lastly head of the OMB, all under G W Bush. Rule Portman out for the reason you already mentioned. Go John Kasich!