After a lot of faffing with possible UI stuff to try to handle moving the contents of the level around in the level editor, I've settled on buttons adjacent to the grid markers in 3D space.
They don't actually work yet, but they look like they'll work better than the half-dozen alternatives I've tried. Now to make them enable/disable depending on whether the level contents can be moved in that direction or not.
In-game level editors are hard!