I think the multi-select in the grid view is what you're looking for to make that easy; both shift-select and control select work when clicking on grid rows. Not the easiest thing to find, but really useful.
You can actually just hold the mouse button down and drag over a pile of checkboxes in the right column. No need to hit shift/ctrl.
Yep, tried it and it works. So if anyone else ran into the same problem, just select all the cases you want to move as described above, then click the context menu button and select "Edit" and you can change the properties for a bunch of cases at once. Pretty sweet indeed.