SOFA for foreigner

I'm in a rare situation. I'm US Air Force stationed in Japan. I met my now wife here in Japan while she was visiting family as she is half Japanese, half Brazilian. We hit it off dating but her visa expired and she had to return to Brazil. We decided we wanted to get married and thought it would make things a bit easier too, in terms of her being able to come back to me. However its proven hard. My question is how do I go about this? From what I have read on another forum here., she doesn't need command sponsorship to receive SOFA status. We got married in the US (she was able to get a visa there and I took leave and met her and we stayed with my parents) and I was able to get her enrolled as my dependent. However, my current tour is unaccompanied and from what the squadron is saying, it can't be changed and she can't receive command sponsorship without being here first for medical screening. I'm stuck and my legal office and chain of command have given me 0 good answers other than what I already know. Thank you to anyone who could help.

If by half-Japanese you mean that she has one Japanese parent, then she should be able to apply for a Spouse/Child of Japanese National visa on her own.

As a dependent, she ought to be able to have her medical screening performed anywhere, and remove this impediment.

Her grandparents are Japanese, shes yonsei and she applied for an long term visa while she was here to try and work towards citizenship but they denied her. Her mother has right to citizenship but she chooses to stay in Brazil. And for the medical screening it has to be done at a military base, a normal hospital in Brazil can't just do the blood work and X-rays, they won't accept it.

Sorry, I missed that she was now back in Brazil. Can she come as a tourist, and get the exam done here?