Florida does not have a reciprocity agreement for Virginia non resident permit holders
The state website also says that non resident holders should check with the reciprocal states to see if the honor non resident permits.
With a permit from Texas I reciprocity with about 27 states. If you are a permit holder from some states Texas recognizes those permits even though they don't honor the Texas permit for states such as California, New York , Hawaii
I really see no advantage to getting a Virginia non resident resident permit.
Have a nice day at the range
NRA Life Member