[...] If the grains are actually "spent"- that is mashed, sparged, and down to under 1.020, the only thing left to extract are flavors from the husks (tannins).
1.020 is too high to stop at. The most used end-gravity target when fly sparging is 1.008-1.010. Batch sparging is a bit different as the gravity changes in intervals with each sparge. And you still would not sparge below that same value.
I know you know this, but for the OP, and the record:
pH is important as the more you sparge the more the buffering capacity of the mash drops. Sparge acidification is definitely needed to prevent tannin extraction, which starts above pH 5.8.
To the OP:
You should taste some of the later runnings and hope to trace some of those flavors and colors you're after. It's pretty thin stuff once you go below 1.020.
So, sparge your mash to increase efficiency. If you batch sparge, do so 2x with half the volume each. Unless you're after a very high OG wort, where sparging is out of the question, you could use the 2nd and subsequent runnings for a small beer or add more grain and do a complete mash for your 2nd beer, again, followed by 2 batch sparges.
There are other ways to make 2 or more beers out of 1 mash. The Nov/Dec 2014 issue of Zymurgy Magazine had a great article how parti-gyling was historically done in England, and way, way beyond today's over-simplified concept. It was common for small breweries to produce 8-12 beers from the same basic mash.
Added:
I see you're doing BIAB, which is typically sparged sparsely, but squeezing is well accepted.
You can run the calculations yourself. After dripping "dry," measure the volume and gravity of the liquid after a good squeeze. That's how much you gained (points). Then weight the wet sack and subtract your grain bill. The difference is the weight (volume) of wort at that gravity which is left behind. Your call to see if it is worth reclaiming with a sparge and/or a more thorough squeeze.