LOI’s are normally “dismissed” with no further action when an airman or their attorney provides objective and credible evidence that disproves the alleged violation.
Per “Pilot’s Bill of Rights”, you have the right to receive copies of all information that the FAA is relying on to generate this allegation. You or your attorney should ask FAA for all the records as you have every right to have them.
Also, if you have not yet done so, recommend you request a copy of your complete Driving record from the NDR. Hang in there!