Stronger Medical Workforce for Veterans Act This bill directs the Department of Veterans Affairs (VA) to develop criteria to designate VA medical centers, ambulatory care facilities, and community based outpatient clinics as underserved facilities. The VA must commence a pilot program to assess the feasibility of providing individuals with tuition and loan repayment incentives to work at underserved facilities. The VA must also ensure that clinical staff working at Vet Centers (community-based counseling centers that provide veterans with post-deployment social and psychological services) are eligible to participate in the VA education debt reduction program. The bill directs the VA and the Surgeon General to enter into a memorandum of understanding to assign at least 500 Public Health Service commissioned officers to the VA.