That said Olivier the information black hole paradox has been an interesting work. The aim was to link the general relativity and the quantum mechanic mainly. The works of Hwking and Bekenstein have been interesting about the fact that we have these radiations. The BHs have an electric charge, a mass, an angular momentum, and in the process of evaporation they have considered these informations.
So I see your idea for the link betweem quantum gravitation, information and mass and energy. We arrive at the real problem about the gravitation. If you consider the lost of informations or the collapses of the waves functions, it is there that we arrive at these philosophical questions about the origin of the universe and if you consider only the GR like cause of this reality, we have problems not renormalisable and unknowns not explained because it is mainly how we consider this origin and main causes of this QM and so how we consider the informations and the gravitation.
If you consider these radiations and the evaporation and the planck scale with the informations, so we arrive at how is stored and encoded an information but we don t know really and like I said the problem is philosophical about what is a primary information and its origin. Wwe dont even know if the siingularitiesw exist and many confusions appear in these reasonings about the storing of these informations and the link with this time even considering the past and future.
That is why the problem is philosophical and how we interpret this GR and the philosophy of origin, if you take the time evolution and the GR , so you intepretat the causalities and localities in function of the philosophy chosen, and that implies specific chosen referentials and so personal intepretations of this gravitation and these informations.If you extend the co ncepts of Gibbs and von neuman entropy , there still it is a ^philosophical choice about the zero entropy and how you consider the evaporation of the BHs and so the informations.
That implies that the informations paradox is just a paradox if you consider the actual limited reasonings of this GR and if you consider only the gravitation of this GR without thinking beyond the box of this GR.It is mainly how you approach the gravitation and the informations and how you consider even this quantum gravitation which is for me a pure newtonian mechanic between massive particles of this standard model and not from this GR with gravitons being the quanta of gravitational waves.
If the informations are not in this reasoning and are not lost in the reasonings of these evaporations of BHs, so the degree of freedom and the violations of the energy momentum conservations and localities are not the key .
The massless and massive particles so become inmportant philosophically about how we approcach the informations and the philosophy of origin of the universe, if you consider the gravitons and the photons massless for example and that you consider the loss of informations in function of energies, it is just a personal choice about this said philosophy of origin of informations, and the bekenstien bound will not change the fact that we have probably deeper parameters to add to this puzzle about the mass, the energy and the informations primary .