with both my pregnancies i had low lying placenta and both times its moved far enough away for me to have a natural birth

i wouldnt be too concerned as everyone else has said they do tend to move

may i also add, both times i was never told to go on pelvic rest, it could be just certain doctors/obs that recommend this but i still DTD and everything and it never made a difference
also not all women experience bleeding when the placenta decides to move either as i never did with either of mine

Goodluck and i hope you get your wish of a natural birth but stay positive im sure you will be fine