Which component is most responsible?

Yes, reasonably clean power however achieved is a must for this as well.

Following up on Brownsfan's suggestion I've picked out a couple of acapella choral recordings you might like (I do anyway) which are probably still in print and might serve your purposes, although I must admit, as I suggested in my first post, that if I were trying to pin down specificity I probably would not use choral music for one simple reason. Choral music tends to be a powerful blend of voices and single voices rarely stand out especially with minimal mic'ing techniques, but even with spot mic'ing, except when used for the soloists. Anyway, here goes....

Rachmaninov's All-Night Vigil, by the Estonian Phil Chamber Choir conducted by Paul Hiller on Harmonia Mundi.

Grechaninov's Passion Week by the Pheonix Bach Choir & KansasCity Chorale conducted by Charles Bruffy on Chandos (SACD)

Sibelius Choral music by YL Male Voice Choir conducted by Matti Hyokki on BIS. This disc has both acapella as well as choral accompanied by orchestra Lahti SO conducted by Vanska. I'm partial to the acapella performances, especially of Finlandia-Hymni a transcription for all male choir of the original, the orchestrated Finlandia. I understand the transcription was to be used by soldiers matching to the war with the Soviet Union in WWII. I still get choked up when I listen to it.

"Which component(s) is most responsible for hearing clear, distinct separation of voices in a chorus or when listening to multiple background vocals, as I often hear audiophile speak of."

All of them.

I think my Polk LSI15’s are limiting me in achieving distinct separation of voices in a chorus.

FWIW, separation of voices in a chorus is very difficult to achieve UNLESS it is in the recording in the first place!

From my experience both of these statements are false. I can create the separation and location in a preamp design no matter what the source, amp or speakers. So IMO and from what I have designed, I can achieve this without the other components and recordings. Just changing the output resistors in a preamp to naked Vishay resistors will provide some of what you are looking to achieve. Filtering your ac inside the preamp will also provide clarity and better separation, and removing capacitors in the signal path will add to the separation, and last using a TVC volume control will add to the separation no matter what the amp, source or speakers are. Sure they other components will improve on this but the preamp can be designed to achieve this.

I believe it comes down to the 2 ends of the chain. 1st, the mic'ing, mixing, and mastering have to capture and preserve the vocal separation. Then, the speakers and room have to allow for the reproduction of what was captured.

The other pieces each play their parts, of course, but I feel to a lesser degree...

-RW-