uh, bark chips maybe?
Actually instead of flooding and draining the seedlings, perhaps some sort of capillary matting set up might be more appropriate to something in a potting mix. I simply have a shelf with liner where there is water in a gutter beside it and the matting hangs off the shelf into the gutter of water to wick moisture up to the shelf and the seedlings sitting on it. Seems to work for seed flats, peat pellets, soil blocks and even small (up to say 10 cm) seedling containers so far. I've also done this on top of a raft without holes too.
uh, bark chips maybe?
I've done compost mix in pots dug into gravel beds so just the bottom inch of the pots touch the water on the flood cycle. Seemed to work for many things except that some critters tended to dig up the pots in search of worms to eat.
You may find that some types of seeds germinate and get going fine while other seeds need more drying. Might be as simple as adjusting the height the tray sits in the bed so the seeds that want drier only the bottom 1/2 cm gets wet while the seeds that don't mind wet could sit lower and the bottom 1/2 of the tray would get wet. Stuff like lettuce will germinate in waterlogged conditions while I think spinach wants a bit more drying. Of course spinach can be challenging to get to germinate well in hydroponic situations.
Here is what I have tried. The mix is 60% fine gravel 40% coconut husk. The mix goes into polystyrene 12 plant trays, and if it works, the seedlings will stay here until transplant into the grow beds. The seedling starter bed is the old duckweed "snack box". It is filled with gravel until the overflow line. The overflow is threaded, and fitted with a threaded pipe full of holes. The idea is that I should be able to adjust the height to which the water rises adequately with this, to have some control over the wicking process. So far, the mix gets soaked right through pretty fast, thus I may have to reduce the height to which water rises in the bed. Still, with the open structure of the media, I may just get away with it. I planted lettuce, carrots, brown and Welsh onions as a first trial today.
I use small rock for germination. I have found that small (1/8-1/4)rock will have a wicking capacity. When using a 2"net pot filled with small rock and sitting in 1/8 of water there is usually enough wicking to keep a seed on top moist. I have found this to be a huge benefit because I cannot water log anything. The seed gets all the moisture it needs and when the roots pop they will get all the O2 they need. I get a very good germ rate this way.
In my case I am using small cinder that was washed out of my GB media. I have played with other small rock and it works similar. This technique works so well that I now germ 90% of my seeds this way. I seed net pots that directly in 2x2 foam sheets with 60 spaces. I give them a 3 day germ in the shade then float them in a sprouting table with 1 inch of water.
Here is more details on my technique.