I've been in your shoes before, take a deep breath, and step back and evaluate. You've not gone past the point of no return... yet. Don't overcomplicate it, keep it simple.
As I said, let them dry out. That will naturally stop the algae and gnats all by itself, dry soil = no food source/not a pleasant environment for them to be in. It will take a few weeks of keeping them drier, but I promise you it will work.
Also/another option (that I have used personally with success), those plants are very very ready to pot up into Solo cups or #1 pots. Pot them up into some fresh drier mix, and don't water the new mix at all! When you set them into the new pot/mix, set them deep enough that you can cover up the top of the existing mix with about a quarter inch or so of the new dry mix. By doing this, you are taking the light away from the algae which will start to kill it, and also the new dry mix will suck the moisture out of the existing mix also killing the nasties and algae and speed up the drying process.
After you pot them up as described above, do not water them for at least 7 days, or only water each plant once you notice the leaves start to become less shiney and or wilt a bit, can't let seedlings completely wilt though as they sometimes don't recover.
When you do finally water them they won't have many roots in that new mix yet, so no need to wet the entire pot, just give them each about 1oz if in solo cups or 2oz if in #1 pots of water via bottom watering and do not water again until you see signs of wilting. Use a shot glass or something to actually measure until you get it down pat. After a while, you can also go by the weight of the pot once you get the feel for it.
Edit: also, I don't think you have BLS or any other problems other than just simply watering way to much. Do not spray them with anything, just try out the process I mentioned above and I would bet money all your problems will disappear by the end of this month.
Best of luck to you this season!
~Troy