Even without the Johnson Scholarship W&L stands a very good chance of being affordable with need-based financial aid. I do think you’d be an excellent applicant for the Johnson Scholarship so encourage you to apply if you apply to the school. My D21 was a Johnson Scholar so feel free to PM me if you have questions about the program or her experience at W&L.
Johnson Opportunity grants and other financial resources are available to support experiences for any student, whether that is study abroad or another project to broaden a student’s knowledge.
While I dont know the strength of Arabic studies specifically I do know W&L had a number of Fulbright, Critical Language Scholarships and other fellowships/scholarships awarded for further study and experience of the Arabic language and culture. As well the interdisciplinary programs in the politics department are very well-respected, with strong ties to DC and industry. Here are a few links to the language and politics departments.
You may also want to look at Mock Convention, Shepherd Program and/or Bonner Program depending on your interests.
Best of luck!