Has anybody done gliding experiments with exact replicas of the birds or other real world flying creatures?
The closest I know of are several attempts to build models of pterosaurs.

Since the head with its long beak is ahead of their center of gravity, the configuration is statically unstable in yaw and needs continuous control corrections. On the other hand, this instability provides very quick responses. This YouTube movie contains footage of a Pterodactyl model made by Paul MacCready in flight. Note that Paul had attached a conventional tail for the first flights to statically stabilize the model in pitch and yaw. Later in the flights this tail was removed. The small skin area between the legs was most likely not sufficient for pitch stabilization, and small changes in wing sweep were used to stabilize the animals in pitch, just like modern birds still do.

Another branch, the Rhamphorhynchoidea, had a tail which provided additional lateral and longitudinal control. Palaeobiologists are still arguing, however, whether the tip of the tail was oriented horizontally or vertically in flight.