The invention provides a device, assembly, and method for transoral endoscopic restoration of a gastroesophageal flap valve. The invention also provides a self-steering and self-closing tissue fixation device for tissue fixation, and an invaginator device for gripping and maneuvering tissue. The restoration device includes a longitudinal member arranged for transoral placement into a stomach, a tissue shaper carried on the longitudinal member that causes stomach tissue to assume a shape related to a gastroesophageal flap, and a tissue fixation device that maintains the shaped stomach tissue in a shape approximating a gastroesophageal flap. The tissue shaper may include a mold. The device may include the invaginator device for gripping and maneuvering esophageal tissue to aid restoration of the gastroesophageal flap, and may include the tissue fixation device.