JR Pass Rules for holders of 2 passports

Hello,

I have a question about whether or not I can obtain a JR pass. I am traveling from the US for a week on business travel (official passport, not a personal passport), but I want to stay a week longer to do some personal travel. I was told that because I had to obtain an "official status" visa, I am not considered a tourist. I do have a personal passport, but was also told that I cannot have two passports stamped when I arrive in Japan that will show "temporary visitor" status.

I will be making several long distance trips (roundtrip Tokyo to Osaka, as well as local Kansai trips) and am finding that it is extremely expensive to pay out of pocket. Is there a way that I can still buy a JR Pass? Alternatively, are there other passes that I can get to help make this trip more affordable?

Thank you for your help.