I would just take out all the rhizomes and start over..
looks like you have different rhizomes planted at different levels, so just adding more soil wont make them all planted properly, some would end up too deep, others too shallow..I would just start over.. at this point, they havent really started growing yet, so it wont bother them to be potted twice within a week or so.
tray method works great! been using it for 18 years..although your containers (in the photos) are a bit large, and the container of water is a bit shallow..
since you are repotting anyway, I would ditch the tall white container..its a bit *too* tall..replace it with a pot that is about the same height as the clear container..then your "tray" will probably be fine..although it could stand to be a bit deeper..aim for containers about 6" to 8" tall, and a tray that will hold 1" to 3" of water..within those ranges will work fine..