You won't know about how your portfolio is viewed until you apply.
PhD students are a very big commitment for a department and an investigator. If a student doesn't finish, the resources the department put into that student are lost.
For this reason, one of the primary concerns for admissions committees when making choices about students is "if we admit this student, will they finish".
Toward that decision, an incomplete Master's degree is a pretty big red flag. I advise that your application should thus try to mollify the committees concerns over the issue, convincing them that if accepted, you'll be in for the long haul. FWIW, I don't think the "I wasn't interested in the work, so I didn't finish" is particularly compelling toward making that case.
So, where does that leave you. There may be programs in your field that don't go by the "let's not lose any students" narrative. They may provide almost nothing in the way of resources until you pass a qualifier exam and find a mentor. Programs like that often eliminate a good portion of there graduate student population at the qualifier. I think your chances for admission are best at an institution like that. Be warned, my perception is that schools have been moving away from that admissions model.
You should also apply to schools that you consider your 2nd or 3rd tier, but with a strong mentor in the area you want to work in. They may not have the same size or quality of applicant pool as your top tier schools, but you'll still get a fine education.
Note that the burden of reviewing the application and admitting a graduate student goes up for nondomestic students, because of the visa issues. Most schools that routinely admit nondomestic students probably have this well in hand, but I do think admissions committees from top tier schools may really try to make offers to only the cream of the crop from the foreign applicant pool.
