Why would there be any downside to organic nitrAtes? One of the points of having plants is to control the nitrAte to a level suitable for the fish. Plants also take up ammonia and nitrIte from the water. NitrAte is their least desirable source of food but in a cycled tank they'd have to I guess.
The point of adding extra NitrAtes is if you have a heavily planted tank with pressurized CO2, because the plants may use all of the one produced by fish. You don't need to dose nitrAtes if your tank is heavily stocked with fish and naturally your nitrAte levels before a water change are at 30-40ppm(that's if your test is accurate) If lowering your nitrAte levels to 20-25ppm is causing algae issues, then you may have an issue with phosphate to nitrAte proportion for example. You will have algae issues if your nitrAte levels go to 0 without you noticing, then the algae will use up the available free phosphates. Same if there's a disbalance between the nitrAtes and phosphates which I think should be in 10:1 or even 20:1 nitrate to phosphate level. Are you dosing phosphate too? Phosphate levels in a heavily stocked tank via fish food can rise up pretty quick, also your tap water may contain a good amount. When you had the algae problems was it all solved by upping up the nitrAte levels? If so, why fix it as dosing up nitrAtes may not be affecting the fish at all at the end of the day. If you still have an issue with algae, then what type of algae did you have on top of cyanobacteria as this can tell you what you are lacking on in the tank.
And to check what proportion of the ppm nitrAte is organic produced, why not test the nitrAte in the tank before dosing nitrAte and after one dose of nitrAte. With such an accurate nitrAte reader it will give you exactly how much ppm nitrAte you just dosed up by substracting the second reading from the first before you dosed. And then multiply this by the days dosed per week, it will give you your weekly nitrAte doses. Then substract that from the total nitrAte in the tank before a water change and the remainder should be the organic nitrAte produced by fish.