So I came up with a solution of sorts. . .
I worked out that the whine is about 16 Khz. As it happens, electronic whine and hum in that range is a problem in the audio engineering industry. And there are solutions.
There's a whole range of products out there for sound-proofing against electronic hums and whines of exactly the sort we're experiencing here. I looked into some of the simpler schemes and they involve wood and cellulose baffling. Long story short, paper towel is your friend.
I wrapped the Crucial SSD in about four layers of paper towel, (the thick, expensive kind), and the sound was deadened by about 80% or more. Good.
I figured a heat sink ought to be included, and I used a narrow strip of tinfoil, (about as wide as the drive and twice as long), used a bit of tape to secure it to the top of the SSD drive and wrapped paper towel around the drive. The remaining tinfoil I folded back over itself so that the little bundle was silver on one side. I used a bit of electrical tape to hold it together, and squeezed it into the drive bay of my laptop, with the tinfoil facing up where it would press up against the metal bay cover. I figured that should be heat-sink enough.
I left out the drive caddy since the bundled up SSD wasn't going to be moving around with all that padding, and closed up the unit.
Now I have a whine-free SSD-enabled laptop.
Cool.
Hope that helps people!