I have a plastic toolbox, approximately 15"x7" outside dimensions. Seven of the round plastic storage boxes from Lee fit nicely in the box with no room to shift around. The turrets with dies fit snugly.
If you don't have the round storage boxes, get a sheet or plank of plywood or plastic (like kitchen cutting board material or Corian counter tops) or aluminum .375" thick.
Cut holes 2.875" in diameter and 8 notches around the circumference to match the notches around your press' turret ring. If you really want to get fancy, install a ball detent just like the one in your press' turret ring. Or make the hole you cut to be a friction fit to make sure your turrets don't rotate to the unlock position. Or figure out some other way to keep them in their "nests".
The sheet/plank should have support (posts or some such) under it to keep it at least 3/4" off the bottom of the toolbox you are storing the assemblage in. Or shelf or whatever.
Just brainstorming here. So another, simpler thought came to mind.
1" thick plank (or plywood or plastic or whatever) with 3" holes in it. The turrets will drop right through, so you have to apply a 1/2" or narrower strip to the underside of the plank. That will keep the dies from falling through and 1/2" will fit between the dies that protrude below the turret.
But you don't want the decapping pin to hit the bottom of wherever you are storing the turrets, so be sure to support the plank high enough. As above, I recommend about 3/4" or more.
In any event, something to keep the turrets from lifting out of the 3" holes would be nice. A piece of upholstery foam would do if there are no powder measures mounted and the turrets are inside a box. Foam, then close the lid.
Latches, like those used to keep screens in your windows would work, but some are a little delicate. If tight enough, a bungee cord going straight across the middle of the turrets, between the dies would also work, or just another straight, solid bar like the one across the bottom. If you are not jostling the assembly around (like, have it mounted to your wall instead of in a toolbox like I do), simple gravity will do.
You could also just secure a row of 3" inner diameter pieces of PVC pipe (with something to keep the turrets from dropping through. Essentially making your own round storage boxes instead of buying them from Lee. Lee's boxes have lids, though.
So much for my rambling thoughts. I hope they are coherent, if not orderly. Good Luck
Lost Sheep
