Check out this site: http://203kcontractors.com/
I looked and there are a couple of contractors in Ohio. I obviously cannot speak to their quality as I have not worked with them; however, by being certified through this company I know they are familiar with the product.
I understand that Wells is much more restrictive about their contractor requirements than other mortgage banks that work with the 203K, so these contractors may, or may not, be certified with Wells. Were you able to get a list of contractors from your mortgage consultant? It seems to me that, if Wells is going to restrict who can, and who cannot, be a General Contractor on their 203K product; they should be supplying their customers with a list of who meets their requirements.
Wells vetting of contractors is a Wells "thing", not an FHA thing. FHA. requires a GC on all standard 203K, they must be licensed and insured, have professional and personal references and be in good standing with the BBB. And, have the financial capacity to front the costs of the project until draws are exercised (this could be cash and/or credit lines with suppliers). I do not choose, nor direct, my clients choice of contractors....and, most lenders would not because of the potential liability. Best of luck to you.