I was born in Virginia, which requires a court order to change the gender marker on a birth certificate.

I am a resident of New York, which does not issue court orders for gender changes.  (They simply want a doctor's letter to do the name change.)

Has anyone tried to change a gender marker on a VA birth certificate for someone who doesn't reside in a state which does gender change court orders?

Unfortunately it doesn't seem like you have many options except moving to a state that does allow gender changing court orders.  The laws have changed quite a bit over the past few years and online information may be out of date, but you could always call the court clerk and see if they have any other options. 

When I started my journey to modify my TX birth certificate there was no online information for obtaining gender change court orders in Seattle, but a few phone calls and emails and I was sent the information I was looking for. 

Good luck.