SOLVED!
On Pickup:
In the pickable item BP:
I. Disable collision of the sphere
II. Disable Physics Simulation of the skeletal mesh
III. Detach mesh from root (keep relative)
IV. Re-attach mesh to the root (snap to target)
In the Character BP:
V. Cast to Character BP and attach to hand (snap to target)
Works in 4.27 (also in Multiplayer via Multicast), gun re-pickable after drop, physics work fine