Yeah at this point the only thing I can think of is just duplicate the object, adjust and render with a mask. While a 'bake' would be an interesting idea I think the whole point of Mesh Element is exactly for that purpose, to give instant randomization as you extend/change the tile arrangement.
Edit:
Oh actually here's an idea. Not sure if it overcomplicates your setup but why not:
1. Use a Multisub as your main material
2. Plug in your current MultiMap into Material ID 1
3. Set the whole floorgen to Material ID 1
4. Polyselect the tile you want
5. Assign Material ID 2 (grey in the screenshot below)
6. Rince repeat for the other 5 tiles.
It just means you cannot change the floorgen later but should fix the issue for now and give you control over those 6 tiles to change them as the client needs (if they want more changes, which is probably lol).

