The goal of this clinical trial is to test an experimental gene therapy in participants with heart failure with preserved ejection fraction, also known as diastolic heart failure. The main questions it aims to answer are: * safety and tolerability of the gene therapy; and * whether the gene therapy helps the heart ventricles relax during filling. Participants will undergo a one-time infusion of the gene therapy in the cardiac catheterization laboratory and then be followed for safety and effects on left-sided filling pressures while exercising. The first year will have multiple in-person visits followed by 4 years of biannual phone calls.