What about one of the Claremont Schools (Pomona, Claremont McKenna, Harvey Mudd, Pitzer or Scripps)? Although each college is small, you can take classes at the other colleges so it gives you the advantages of both a small and medium-sized college.
There are only 60-ish schools that meet full demonstrated need- I googled "colleges that meet full financial need"- and a handful of others that meet 90-99% of financial need. So, you may want to start with that list and see which top engineering schools are on it (I know both Lehigh and Bucknell are) and which ones offer merit aid, as not all schools do offer merit.
I have a MA and am starting a college counseling certificate program mid-Sept. Very excited- now when my husband asks if I am on College Confidential yet again I can tell him it's all in the service of my future job :)