Finally, two exceptions to "Rule 47" have been claimed to allow killing prisoners.

One is fairly obvious and generally permitted - CIHL, v. I, pp. 230-231 pdf:

Loss of protection

According to Additional Protocol I, immunity from attack is conditional on refraining from any hostile act or attempt to escape.[59] This is also set forth in several military manuals.[60] The commission of these acts signifies that the person in question is in fact no longer hors de combat and does not qualify for protection under this rule. The Third Geneva Convention specifies that “the use of weapons against prisoners of war, especially against those who are escaping or attempting to escape, shall constitute an extreme measure, which shall always be preceded by warnings appropriate to the circumstances”.[61] The Convention contains other specific rules applicable to the escape of prisoners of war.[62] Hostile acts have not been defined, but the Commentary on the Additional Protocols gives examples such as resuming combat if the opportunity arises, attempting to communicate with one’s own party and destroying installations of the enemy or one’s own military equipment.[63]
The other (that special circumstances allow prisoners to be killed) is more controversial. In the CIHL view, and in US doctrine (upon which that CIHL view is heavily based), that COA is banned. E.g., p. 230 pdf:

Quarter under unusual circumstances of combat

The prohibition on attacking a person recognised as hors de combat applies in all circumstances, even when it is difficult to keep or evacuate prisoners, for example, when a small patrol operating in isolation captures a combatant. Such practical difficulties must be overcome by disarming and releasing the persons concerned, according to Additional Protocol I.[53] This is restated in several military manuals.[54]
Here, CIHL cites and quotes FM 27-10, The Law of Land Warfare (1956, rev. 1976) (currently in effect):

85. Killing of Prisoners

A commander may not put his prisoners to death because their presence retards his movements or diminishes his power of resistance by necessitating a large guard, or by reason of their consuming supplies, or because it appears certain that they will regain their liberty through the impending success of their forces. It is likewise unlawful for a commander to kill his prisoners on grounds of self-preservation, even in the case of airborne or commando operations, although the circumstances of the operation may make necessary rigorous supervision of and restraint upon the movement of prisoners of war.
FM 27-10, The Law of Land Warfare, applies to US Soldiers and Marines.

That ban on "special circumstances shootings" goes back a long way in US doctrine - e.g., the 1914 US Rules of Land Warfare:

68. Execution of. - Prisouers of war may be fired upon and may be shot down while attempting to escape, or if they resist their guard, or attempt to assist their own army in anyway.[1] They may be executed by sentence of a proper court for any offense; punishable with death under the laws of the captor, after due trial nnd conviction. It may well be doubted whether such extreme necessity can ever arise that will compel or warrant a commander to kill his prisoners on the ground of self-preservation.[2]

1. They should be summoned to halt or surrender before firing. (Hague Con. 1899 Pt I, pp. 86, 87).

2. G.O. 100, 1863, art 60, in referring to giving of quarter says: "But a commander is permitted to direct his troops to give no quarter in great straits, when his own salvation makes it impossible to cumber himself with prisoners." The German Kriegsbrauch of 1902 says: "Prisoners can be killed * * * in case of extreme necessity, when other means of security are not available and the presence of the prisoners is a danger to one's own existence. * * * Exigencies of war and the safety of the state come first and not the consideration that prisoners of war must at any cost remain unmolested." No instance of resort to such executions have occured since 1799, when Napoleon bayonetted the Arabs at Jaffa.
The last sentence may or may not be accurate.

Such is the current state of the law according to the best sources I've found.

Regards

Mike