Does placing a piece of tissue inside the vagina—such that it covers the inner vulva and the labia majora are pressed against it—prevent secretions from reaching the outer vulva, and thus validate ablution for a longer period?

Vaginal discharge is pure (tahir), and there is no obligation to guard against it. Ablution (wudu') is not invalidated except by its exit to the outer vulva. If there is doubt about its exit, the original state is that it has not exited. There is no need to inspect to verify its exit. If you doubt the time of its exit, attribute it to the closest probable time. There is no obligation to use a pad, and do not rule that your purity (tahara) is invalidated merely by doubt. Your past prayers are valid as long as you have not ascertained the discharge's exit to the outer vulva.