Check with your GC at the Governor’s School. They should be able to give you some ideas on where you might get the kind of scholarship you are looking for. This is a well regarded school and the GC’s should be quite knowledgeable about the college admissions process - they are quite invested in getting their students into good college situations. It’s kind of their reason for being, kwim?
That said, also check with them and make sure that UVa and VT are indeed safeties for you. That may sound far fetched, but I know students from TJ (Thomas Jefferson High - one of the best HS’s in the country) can have trouble with those 2 schools …VT and UVa can’t take the entire graduating class, even if they’re qualified. So make sure you’re OK if you want to use them as your safeties. The GC’s are probably the only ones who can give you that info, because everyone else will assume with your resume that you’ll be a shoe-in for those admissions.
ETA: think carefully if you’d be ok with a full ride to less regarded school than UVa or VT. That may be your trade-off.