Anonymous kindly provided Comments on November 2018 on deep diving submarine research to test Stirling AIP capabilities.
Concerning the Kockums Stirling air independent propulsion (AIP) system known as the v4-275R, "v4" means V4 engine and "275" means a cylinder volume of 275cc. The pressure after combustion is 22 bars and waste gases are evacuated directly into the seawater. This means seawater pressure cannot exceed the 22 bars exerted at a submarine diving depth of 200m.
Further on the Stirling v4-275R Gas of work: Helium (130 bars). Speed 2400 rpm. Fuel consumption 260 g/kWh. Oxygen consumption 980 g/kWh. Maximum power 75 kWh. Recoverable heat from the combustion gases 18 kW. See [1].
DEEP DIVING RESEARCH ON STIRLING AIP
1. SAGA Submarine
[1] The French built SAGA submarine is the first prototype of a new generation of industrial submarines capable of carrying out underwater operations using divers or robots at close proximity to the work site without surface assistance. SAGA is equipped by a diesel engine and two Stirling engines (Kockums v4-275R, 75kW) for surface and submerge, respectively. scroll half way down http://www.robertstirlingengine.com/saga_uk.php
At the SAGA submarine, symposium ISM 90, the 3, 4 and 5 December 1990 in Toulon, J. Mollard and D. Sauzade, which states "The waste gases, being at a pressure of 22 bars, are evacuated directly for immersions lower than 200 meters. Beyond and until the maximum immersion of the SAGA (600 meters), it is necessary to pressurize these gases and the condensates, which required the development of a specific compressor produced by GIE SAGA."
See photos of the yellow SAGA deep diving research sub at H. I. Suttons Covert Shores http://www.hisutton.com/Comex%20Sagittaire.html
2. Japan's DSV Shinkai 6500
The DSV Shinkai 6500 is/was designed to dive to 6,500m where pressures of 650-700MPa are experienced (Unit Converter 1 Bar = 0.1 megapascal (MPa).
Using DSV Shinkai 6500 research on a Stirling engine combusting at high pressures was conducted years ago. An AIP combustion of 70MPa was achieved.
It is unclear if research finished. So, an increase in combustion pressure for the Kockums v4-275R may be possible to achieve higher efficiency and deeper diving.
See youtube on Japan's Shinkai 6500 deep submergence vehicle (DSV). It is arguably the world's deepest diving research submarine. It has a Titanium pressure hull.