Thank you for the follow-up. Most lenders these days are using Deeds of Trust, which are slightly different from mortgage instruments. Those start with the borrower buying the property getting a warranty deed in their name, then the lender immediately recording the deed of trust which encumbers the property and lets the world know that there's a loan on the property.
When the loan is paid off, the lender records a Deed of Reconveyance, which officially notifies everyone that the loan is paid in full and there is no longer a lien on the property.
I was thinking that the FL approach with the "Satisfaction of Mortgage" being recorded has the same effect as (or was a different name for) a Deed of Reconveyance. Here is Florida's law on the subject:
Section 689.07 there authorizes Deeds of Trust and sets the rules of what happens when a satisfaction of the debt is obtained and recorded. This part of Florida law sets up the usual type of Deed of Trust situation which is most common these days.
I cannot tell from your question whether your mortgage was on a Deed of Trust or the older legal framework. But regardless, the Satisfaction of Mortgage document is supposed to be recorded in connection with the land no more than 60 days after payoff. That document evidences payoff of the lien. IF there are no other liens, then the landowner can convey good and marketable title. Running the transaction through a title company will include a title search which confirms the status of the property, and will include title insurance to pay to defend title if something funny happens later on.
As far as proving you did not take out another mortgage on the same property, that's what a professional title search is for.
A title company can help you with that "another bank had a lien" problem. IF that one is paid off more than 60 days ago, and no satisfaction of the lien type document has been recorded, then that lender is responsible for any damages the borrower sustains from that failure--like being forced to hire an attorney to get the title cleared up because of that failure.
If a person wants to transfer property with a warranty deed without first getting a title report and title insurance, then they by themselves are on the hook to defend title if there is some undisclosed lien against the property. Marketable good title can be conveyed "subject to" a prior lien--it happens all the time though it is not the majority situation. There is no legal requirement to have all liens cleared out before transferring land, except for liability if something false is said which is important to the transaction, or something is concealed or not disclosed to the buyer/grantee (not everyone getting land actually buys it).
You will need to go back to the original purchase documents before all the refinances and check again for a deed of some sort. IF the prior owner did not warranty title or include title insurance in that original purchase transaction, then title insurance for a later warranty deed might cost some more--but that is a non-legal matter of what risk level the insurance company sees there and is willing to live with.