That sounds like a fun project. From what I understand, the most warping is going to happen right away when you cut it into smaller pieces. I’m assuming it was kiln dried, because almost all is. There’s some interesting info about it in this video:
I think the one on the left would have better looking grain if you cut it horizontally, but that may be my opinion. If you cut it vertically, it will just be a bunch of parallel lines. But I would guess it’s more likely to warp if you cut it horizontally… The one on the right is the same either way.
The one on the left is quatersawn which is great for strength but not all that great to look at. If you want something nice to look at you would want to cut it diagonal to through the grain. Cutting it vertical to how it sits there will make it the most stable but also the least attractive to look at. Cutting it horizontal with the grain lines might look a little better but might not be as stable. Theres tension in wood and you won’t really know exactly what its going to do every time you cut it. You can make probable guesses. Do you have a moisture probe? You can figure out a little more what its going to do if you know the moisture content vs the humidity of where you are. Thin pieces like that are sometimes a gamble. I had one that was around 6mm that stayed perfectly flat for over a week. I went to put some polyurethane on it and it curled up pretty bad.
Are they wax coated? Were they machined locally? If they are wax coated and imported from far away when you cut them who knows what will happen. I’ve had some import I didn’t scrape and then let slowly stabilize to my environment and they split right up the middle.