Read the book "The College Solution" (2nd edition) by Lynn O'Shaughnessy. She is excellent on the money issues especially in how to target a school that will give your child merit money. She also advocates that you find good academic and financial fits for your child. Like you said it is ridiculous to have your child apply and get accepted to school which you later find out you cannot afford.
A good way of targeting a school for merit money is to focus on schools where you son falls within the top 25% to 33% of the applicant pool. For this reason it is good to have the matches and safeties on your son's list be those type of schools. Still very good colleges but just willing to give out more merit money. We used this methodology and our son ended up with close to $750K in merit scholarships including 2 full rides. He currently is at Ohio State and loves it and has a full-ride. It looks like your son would qualify for the OSU's buckeye scholarship which would give him $10K a year.
Others have mentioned it but be sure to run your numbers in each schools "net price calculator". This calculator is part of federal legislation which required colleges make a student's true price more transparent. Now all net price calculators are not "created equal" so some may include a merit award in your calculations and others will not.
The other thing to look at is a college's "common data set." This information breaks down admissions information to a great deal. If you look at the section on financial aid and merit scholarships you can learn how generous a school is to incoming freshman. For example Richmond's Common Data Set http://ifx.richmond.edu/pdfs/CDS_Section%20H.pdf
says that 100% of financial need was met and that the average award was $39387 of which only $5K was loans. For merit aid which they classify as non-need based awards the school gave out 56 awards which averaged $36800. In contrast Wake Forest gave 49 merit awards to a larger entering freshman class but the award only averaged $16500. http://www.wfu.edu/ir/docs/cds2011wfu.pdf
This information would tell you that Wake Forest is not generous with merit money and that your son would get a better deal at Richmond.
Some schools have scholarship calculators such as Baylor which will give you a more accurate picture.
Be sure to look at the financial aid forums and the forums for each individual colleges.