How To Deactivate Physics On Skeletal Meshes For Random Poses

I am setting up an atmospheric nighttime scene, including dead bodies the player discovers. What I want to do is suspend skeletal meshes in the air in the places where the bodies will be found, and have some sort of delayed deactivation of the mobility of the meshes to keep the poses they end up in after game start. Basically, have it such that when the game starts, the skeletal meshes will fall and end up in a random pose, then after a few seconds will become frozen in that pose.

The problem I’ve had is that if I deactivate physics on the skeletal meshes, they revert to the straight, stiff mannequin pose they started in, usually with part of the mesh clipped into the ground from when the mesh was changing orientation while physics was active. It would be easiest if I could just leave physics on, but this leads to the meshes getting “kicked around” more than I’d like by the player character, as well as causing an erratic view rotation/teleportation of the player character.

How can I best set this up so I get the random poses I’d like from the meshes without any of the various collision issues I mentioned? Looking for a solution that doesn’t involve manually posing the meshes if possible. Thanks.