@MikeF, I took a look at the two SLDs with the highest population in that database: 1871 and 1860-S.
My analyses for the low, medium and high bullion periods I used earlier agrees with your conclusions. I also went back a bit in time before the "spike" in silver prices, picking a period that was comparable in silver price to the more recent "low" period. The dynamics at the two price points are a little different
For the 1871 I looked at XF40-45:
Low bullion (5/17 to 5/18), median selling price was $444
Med bullion (7/13 to 7/14), median selling price $505
High bullion (2/11 to 4/12), median selling price $518
Low Bullion (1/08 to 6/10), median selling price $374
This coin at this grade looks like it moved in tandem with the upswing in silver price, then dropped back down. The 2008-2010 number is depressed a bit by a handful of NGS graded coins that all fell at the low end ($250-350). Without them, the median would be more like $400
For the 1860-S there are more higher graded coins in the database, so I looked at MS62:
Low bullion (5/17 to 5/18), median selling price $1870
Med bullion (7/13 to 7/14), median selling price $2230
HIgh bullion (2/11 to 4/12), median selling price $2300
Low bullion (1/08 to 6/10), median selling price $2300
So, this higher value coin took off when Silver passed about $10/oz, plateaued for about 6 years regardless of silver price, then dropped recently.
That's still only 4 coin/grade combinations, but suggests the picture is much more complicated than "low value coins move with bullion price and higher value coins don't."