Are there potential issues with a dual citizen purchasing Japanese real estate using their American Citizenship?

I am purchasing a second home in Japan, but I'm concerned about potential issues stemming from dual nationality. I am unable to purchase the property as a Japanese citizen, as I do not have an inkan shomeisho or a juminhyo. So it seems like the best way for me to purchase the property would be as an American citizen, as that would remove these legal roadblocks to signing the contract. If I were to move to Japan full-time in the future, and I enter the country with my Japanese passport, would there be issues with living in my house?

Would I need to re-register the property once I get the requisite documents? Would I even be able to? Both my passports have the same name in english.

What would the tax situation be like if I start working full-time in Japan?

I figured this would be the best place to find people knowledgeable about property ownership and complex tax situations for dual citizens.