Hm. Quoted in the linked post is the fact that Dumbledore's suggested revision to the Potion of Eagle's Splendor (the one that would end up making the imbiber sick for weeks, as happened to Petunia) was, specifically, replacing blueberries with Thestral blood. Now where else has that come up recently?

And Harry knew, now, that the concealment of the Cloak was more than the mere transparency of Disillusionment, that the Cloak kept you hidden and not just invisible, as unseeable as were Thestrals to the unknowing. And Harry also knew that it was Thestral blood which painted the symbol of the Deathly Hallows on the inside of the Cloak, binding into the Cloak that portion of Death's power, enabling the Cloak to confront the Dementors on their own level and block them. It had felt like guessing, and yet a certain guess, the knowledge coming to him in the instant of solving the riddle.

Considering that by the time he annotated Lily's book, Dumbledore had certainly had around thirty years to study the Elder Wand (which canonically has a Thestral tail-hair core), and may or may not have already examined the Cloak of Invisibility as well, this certainly seems suggestive of something. I've no idea what, though. ("Charming as death" doesn't seem like much of a compliment.)