This is not an knowledgeable answer, so forgive me if this is irrelevant.

The paper, "Random sequential adsorption," by Jens Feder (Elsevier link), seems to indicate that "the size distribution for non-overlapping holes" is known, which, at least superficially, seems to relate to the quantity you want to compute...?

Abstract. By placing at random disks onto a surface, but adsorbing only those that do not overlap previously adsorbed disks, one will finally reach the jamming limit beyond which no more disks can be adsorbed. We find, using computer simulations, that the coverage at the jamming limit is θ = 0·547 ± 0·002 for disks and θ = 0·562 ± 0·002 for aligned squares. For the jammed state we have evaluated the pair correlation function for the disks and the size distribution for non-overlapping holes. [...]

This is not an knowledgeable answer, so forgive me if this is irrelevant.

This old paper, "Random sequential adsorption," by Jens Feder (Journal of Theoretical Biology, 87(2), 1980, 237-254 Elsevier link), seems to indicate that "the size distribution for non-overlapping holes" is known, which, at least superficially, seems to relate to the quantity you want to compute? Surely there has been more recent work.

Abstract. By placing at random disks onto a surface, but adsorbing only those that do not overlap previously adsorbed disks, one will finally reach the jamming limit beyond which no more disks can be adsorbed. We find, using computer simulations, that the coverage at the jamming limit is θ = 0·547 ± 0·002 for disks and θ = 0·562 ± 0·002 for aligned squares. For the jammed state we have evaluated the pair correlation function for the disks and the size distribution for non-overlapping holes. [...]