You can fit, like, a gazillion of them on the head of a pin so they shouldn't even feel much in the way of tidal forces. Don't Angels have teleportation powers anyway?

Not in the LDS perspective. For us there are three (sort of five) types of angels. There are the spirits of people that haven't been born, the spirits of people that are dead but not resurrected, and the people that have been resurrected. The other are people sent from God that are not dead, being both those that are mortal and those that have been translated. The mortal one is uninteresting, one could probably find a grad student willing to do the experiment with the promise of a PHD. The others are the more interesting ones, being what effects does gravity have on spirit matter (being that for the LDS spirit is a type of matter) and what effects would it have on a resurrected body or a translated body. Destruction of the spirit is not a possible outcome. I have determined that, unfortunately, God is not likely to allow test subjects to volunteer themselves for the experiment and/or provide a convenient black hole for said experiment. Presumably once one is resurrected one will gain that knowledge.

Something like Teleportation, I am unclear on the details.