As to preference points and the draw, I've been one lucky SOB applying out of state, so who knows with someone in the Ia draw. Some of the lower pressure zones you could draw first time, but these probably have the least amount of deer/public land.
I also mirror the sentiment already posted in regards to the "well managed" part of your post. Public is public, not known for "trophy" management, more like herd management. Best bet would be a trip to knock on doors to try to gain access to private with public as a fall back. I would suggest that you make the knock on door trip before fall. As a landowner/hunter, those knocking on the door the week of season opener get the biggest NO!