Without knowing more facts and reviewing the documents, it would be difficult to see how your would prevail a suit against "one of the five big banks." You borrowed money to buy a house. You did not pay back all of the money thay you borrowed. The lawyer who could give you the best advice on remedies open to you is the one who represented you in the deficiency judgment lawsuits.
Disclaimer: This answer is provided for informational purposes only, does not constitute legal advice, and does not create an attorney-client relationship. Actual legal advice can only be provided after completing a comprehensive consultation in which all of the relevant facts are discussed and reviewed.
You also don't mention when the lawsuits were dismissed. You might have a cause of action for fraud, but without a review of your pleadings and more facts, it is hard to determine by posting a question on a website. You will need to contact an attorney in your area that understands not only real estate and mortgage foreclosure defense, but is able and willing to challenge the banks in court, probably federal, with a fraud action.
This communication is not intended to create an attorney/client relationship. It is always recommended you consult an attorney in person to discuss your case. The Law Offices of Stage & Associates practices state-wide and represents homeowners and community associations. Please visit our website at www.stagelaw.com.
What are your damages that you want to sue for? If you had the deficiency suits dismissed you likely should have been able to recover your attorney's fees and costs (assuming the lost notes had a provision for the award of fees). What other losses do you claim that you think you can recover? You have to answer that before anyone can tell you if there is a theory upon which you might prevail, which at this point seems unlikely to me.