If you know that you are not eligible for need based aid, and your child does not throw long, have a good rushing game, does nothing but net from the top of the key, or is a world class track and field person (in other words, you child is not a Div i recruited athlete) then you need to let your child know, how much you are willing to pay.
As @thumper1 says, then your child needs to look for scholarship (best ones coming from the school to help bring the cost down). You should be looking with him/her. Don’t have them doing all of this legwork for if you are not willing to pay the balance.
If all you intend to pay is no more that the cost of tuition at the local college while kiddo lives at home, s/he needs to know that now. This way they can look at schools that will not cost more than the budget.
So far it looks like Oregon is not a financially feasible option because you are not willing to pay the OOS cost.