UNC and UVA are both high reaches. Although your stats look good, a 92% GPA, non top 10% rank, and lack of rigor (e.g. no physics, no honors science) aren’t top tier which you have to be to be admitted to UVA and UNC as an OOS student.
Also, as you said, neither UVA nor UNC has direct admit business. At UVA, one can do everything right (straight As, join clubs, etc) and still not be accepted to McIntyre because the process is holistic and they build a diverse class. What would be your plan B if you aren’t admitted to business at either school?
If you like Richmond, look at Bucknell, Lehigh, and Villanova. You would be direct admit at IU Kelley so take a look at that. Also adding SMU, UMiami, and Tulane…but Kelley is better in terms of business than all of those.