First off, 'a large party,' even used by the same author, can mean more than one number range. A large party in a small dining room would to my mind be very different from a large party at a ball, or all going on a picnic together.

Second, at a dinner party, you are not simply able to hear a conversation X yards away from you, and not to hear it if it is further. There are other conversations going on between Elizabeth and the head of the table. There could be the background noises of servants; outside sounds from open window; the roaring of a fire (likely not in summer); certainly glasses clinking, plates and utensils in motion, guests shifting postures, and dishes being passed would be almost continuous.

Third, the passage about the two eldest Bennet daughters pouring out tea and coffee implies that a gentleman would not be able to stay (without being conspicuous?) near the table unless seated, as perhaps the ladies already are. So, a moderate number of seats could effectively cut Elizabeth off from a sustained conversation with Mr. Darcy - she only need have a lady on each side and one across the table from her, and she is hemmed in by a crowd. Three is a crowd, sometimes!

Fourth, even were they seated within 15 feet of each other during the card play, one of them could say 'my side of the room;' that phrase may not imply that each was shunted into a corner the farthest reach from the other. In Mansfield Park, Sir Thomas as a whist player is separated from his wife, Lady Bertram, as she learns the game Speculation at another table. There is no implication that the room or the party in it are large, or that the tables are far apart. Yet, the implication that each table has its own atmosphere, distinct from the other, is clear. I am not sure that Mr. Darcy being seated at a whist table and Elizabeth being seated playing another game means that there was (to exaggerate) a stadium full of people between them.

On the other hand, from the hints you have collected about the 'large party of friends' at Pemberley, you have created a new view for me. I am willing to believe that the Bingley party was not the only set of guests that visit, and that Author Austen decided not to cloud the issue with naming one-off characters that did not move the plot forward.