Rebeccian
It is definitely possible as I backed a couple of winners today (and a couple of losers!) to place with SportOdds.
It is not always possible for all races for all courses. I managed to back them at Port Macquarie today and I would think that most of the metro races would be allowed. You have to wait until 20 minutes or so before the race (I don't know the exact time) and then you are offered 2 buttons for each horse, a Win button and a Place button. Hit the Place button and a pop-up window then allows you to enter your bet for Place only.
Give it a go tomorrow.

It will always be difficult to beat the Betfair odds but at least you know they are fixed and that your bet has been taken.