Can you live with rust? Lasers and rust don't mix but plasma doesn't have much of an issue with it. An outside storage rack is an option, though certainly not ideal. I'm not sure about your climate, but here it would be more the condensation cycles that cause the rust rather than the direct rain.
Something else I was thinking about after my other post was to have some sort of "tilting shelf/rack". Something like the rolling cart that you had mentioned earlier, but with a tilting mechanism to allow you to pick sheets from it horizontally with the forklift. At the same time you can save space by tilting them vertical for compact storage. You'll be limited in capacity by the overall size and weight but it might work if you just want a sheet or two of different thicknesses to keep in stock. You'll have to be careful to keep it balanced and/or mechanically supported in rotation for safety. Though if you can figure out how to keep the center of gravity ... well, centered, then it might be as simple as a large gas spring, threaded rod, or gear/crank.
The key to storing sheets is that as soon as you have one heavy sheet laying directly on top of another it's a PITA to get the forks between them without damaging them. It can also be a hassle to pick up just the top one with a magnet, as the next one or two are attracted as well. You need to get a prybar in there and "pop" then apart quickly. The design would need to have separators that allow you to pick individual sheets. You also need to account for some extreme bending of thinner sheets' ends under their own weight on narrow forks. You can get away with keeping one or two along with a more rigid (1/4 or 3/8 maybe) sheet that doesn't allow the ends to sag when you're trying to insert it into a narrow shelf space. Then you just pick up the pile, bring it over to the table and hand-bomb the thinner sheet from on top without too much trouble. Alternatively, you pick out a thick one and bring it right under the storage space for the narrow one and slide it out on top. Opposite for putting it away again.
Now that I've mentioned it, I'm thinking this is likely along the lines of what Dave (redshift) was suggesting with the "car roller" (though in fewer words). When I read it I was thinking "dollies", but I think he meant more like a car "rotisserie". I don't know what types are available - whether they have a pivot point and stationary base, but I know I've seen at least one that would require a lot of floor space to roll over.
If nothing else, maybe this will get you thinking about the problem another way and spark an offshoot idea. It all helps. Judging by the other "big" projects you take on, I'd say such a gizmo should be fairly easy for you to manage (in an afternoon or two :P ) .