According to R' Moshe regarding the location of the Bimah in a shul, what is defined as the "center" of the congregation?

Question

This is based off of my lengthy answer here regarding the location of the Bimah in a shul. As a result of that research, I was left with one question.

In that answer, I quote R' Moshe Feinstein in Igros Moshe OC 1:42, who says:

בדבר הבימה אין קפידא שיהיה באמצע בית הכנסת ממש, וכמעט שעוד עדיף שיהיה קרוב יותר לפנים, דברוב פעמים אין המתפללין ממלאין כל ביהכ״נ ועומדים רובם יותר קרוב לפנים וממילא צריכה הבימה להיות באמצע עמידת המתפללין כיון שעיקר הטעם הוא כדי שישמעו העם קה״ת.

Regarding the Bimah: We aren’t particular that it should be literally in the middle of the shul, and if anything, it’s better that it should be closer to the front, since many times the congregants don’t fill the entire shul, and the majority of them stand toward the front, and it comes out that the Bimah needs to be in the middle of where the congregants are standing, since the main reason is that the congregation can hear the reading of the Torah.

And I inferred from there:

While I don’t know that the logic of R’ Moshe would apply to every shul that it should be toward the front rather than the back, the underlying logic would remain: wherever congregants tend to stand when the shul is only partially full, the center should be where the Bimah should go.

Based on the above, what defines the "center" of the congregation? Let's say that 90% of the congregation is in the front, and 10% is in the back, with a wide gap in between them. If I were to draw a shape that perfectly encompasses all congregants, the center of that shape would roughly approximate the actual center of the room. On the other hand, 90% of the congregation is in the front, so perhaps the Bimah should be further toward the front, in the mean center of the population.

I am asking specifically according to this understanding of R' Moshe. I don't want answers according to other opinions. I will accept answers that can prove my assumption wrong, though I would rather an answer that can demonstrate from a different teshuvah of R' Moshe if he addresses what he means by the center.

Answer 1

I'm inferring that when he says "the majority of them stand toward the front", it may be that they do this because the amud is at the front of the shul and this where the chazzan davens from. (Rav Feinstein does state that the chazzan may daven from the bimah if people can hear him better from the bimah.)

Thus, since the majority of the time people are listening to tefilla done by the chazzan, rather than Torah reading done on the bimah, Rav Feinstein suggests that the bimah be placed in the middle of where the congregants are, namely physically more towards the front of the shul rather than specifically the geometric center of the shul. This way, people have the advantage of equally hearing the chazzan as well as Torah reading.

However, it seems that Rav Feinstein allows a leniency in that if the bimah happens to be in the geometric center of the shul, and people cannot hear him from the amud, then, he can daven from the bimah. To me, that implies that, with a small minyan, people should probably crowd around the amud to hear the chazzan best, as, ideally, he should daven from the amud. However, when there are many people, and thus, this is impossible, then, he allows the chazzan to daven from the bimah if it is in the geometric center.

In summary, Rav Feinstein implies that ideally, the amud and bima should both be near the front of the shul. I rarely see this configuration, but, then, again, the shuls that I generally attend are in large buildings many of them close to a century old. When these shuls were built, they were regularly full, so it made sense to have the bimah in the center. (I won't delve into the reasoning as to why the chazzan is in front and Torah reading is in the center.) With a mostly empty shul during the past 30 years, roughly, if it were feasible to move the bimah toward the front, I guess, they should be doing that. Perhaps, this begs the question as to why the chazzan still davens from the amud or why most of the people scatter themselves around the shul when they have trouble hearing him. I guess the concept of following other people's "Amen" response is sufficient.