You're pretty lucky that your tank cycled in only three weeks. But even so...you have an extremely heavily-stocked 30-gallons of water, and the stock in it is very heavily fed, so crazy nitrate levels are, IMHO, to be expected. Expecting plants to be much help is likely a pipe-dream in this case; the total mass of plant matter needs to exceed that of the animal matter by a huge margin, and that won't be the case in this tank.
Nitrate levels that high can't be doing those fish any favours, and that in turn means that they aren't the healthiest, best food source for your turtles.
If it were my tank, I'd take out all of the fish and just keep the turtles. This would allow you to do 100% water changes without any worries about chlorine, pH, etc as long as the temp is about right, and I'd do at least one of those per week. I always remove aquatic turtles from their tank to be fed in a separate smaller container, then place them back into their main tank after they have eaten and, ideally, also had a big bowel movement. Turtles produce massive amounts of ammonia and other waste, so this practice keeps the main tank much cleaner, much longer. But, of course, everybody wants to watch an Alligator Snapper "fishing" for its prey, so if you insist upon that you will have to feed them in the display tank and accept the extra cleaning that goes with it.
In any case...you will be needing to upgrade that tank size soon. These guys don't grow as fast as something like a Redtail Catfish...but they do grow pretty quickly and will soon outgrow that tank.