Don't get your hopes up with the floating plants
@Dr Um because they won't bring your nitrates down drastically.
I use the API test kit, and when I test tank nitrates, and compare the colour to a tap water sample, the tank sample colour is slightly lighter than the tap water sample, but not enough to take it down to 20ppm, for example. However, I have found that the floating plants do help, and stops the nitrates getting any higher.
If you have concerns about the cories, the answer (in my very limited experience) is to use a mix of tap water and RO water to recreate the water parameters that the fish need.
Saying that, please keep in mind that a lot of fish that have been commercially bred for a considerable amount of time have become more tolerant of a wider range of water conditions, but tolerant is not the same as the fish thriving. It is quite a complicated and controversial topic, that I don't plan to go into here.
However, I will say that my tap water is relatively hard, with high nitrates, and I have peppered cories in my temperate tank, and panda cories in my betta tank. Both groups appear to be doing well, and have reproduced.
Speaking to staff at my independent LFS, and their main suppliers (who also breed certain fish) have harder water than we do here.
I use a mix of RO and tap water in my river tank because at least one species of fish in that tank is wild caught, as far as I know (another controversial topic that I'm skirting around and moonwalking away from).
So, apologies for the rambling response, but I just wanted to make sure that you would know that floating plants are not a miracle "cure" for your nitrates, but will help, and that your water conditions will not necessarily keep you from keeping the cories that you want, but you may just want to ask your LFS where they have come from, the conditions that they have been kept in, etc (also bearing in mind that it is almost certain that your LFS has the same water conditions that you have at home).
Keep us posted on your progress.