Obviously you can't tell us what you are doing for your Fulbright here, but keep in mind the details you redact here are very important to your chances. Admission is not dependent on the transactional nature of experience hours without context.
To answer your question, an "X-factor" like a Fulbright doesn't supersede typical GPA/MCAT metrics, but we're missing our overall GPA trend (year by year) and can't see your transcript. If you are doing more teaching like your described non-clinical volunteering (afterschool program), you may not have enough service orientation activities. Teaching, tutoring, and mentoring are academic competencies that highlight your expertise as a learner. Service orientation activities include food distribution, shelter volunteer, job/tax preparation, legal services, transportation services, and housing rehabilitation; you should have 150 hours when you submit your application or you risk getting screened out at most schools.
Research is also a reflection of academic competency. But Fulbright research is very broad and could involve service. Without a full description, it's too hard to know whether this helps you as much as you think it would.
You also should apply to DO schools as your GPA/MCAT is competitive. They may be a bit more impressed with the "Fulbright," but service orientation is still important.
However, you are well-suited for research careers (PhD), and they will be impressed with your Fulbright (in all likelihood). Your above description doesn't give me an impression you are passionate about medicine due to your lack of details on your clinical experience. The transactional description tells me you're confirming a checklist of activities for a strong application, and your hours and accomplishments are more weighted to research milestones than serving your community.