I think there are some pieces of advice that may be applicable and some pieces of advice that may not be applicable to your situation in this thread.
First, to answer your question, carbon will not remove the nitrate.
Second, the removal of nitrate from your system will approximate the percentage of water change. Therefore in your 32 gallon, if you change your 40%, you should expect your nitrate to drop by ~40%. This isn't always apparent when we measure it as many test kits are hard to discern smaller changes - for example the API nitrate uses shades of red- these can be difficult to discern from each other and changes may only be apparent once you've fallen under a certain level - almost like the value "rounds up" to your eye when it's between two values.
Therefore, there are still two options- one is that you need further water changes to lower the level tr be able to discern the lowered level on your test kit. The second is that there is still an input of ammonia. It's possible there is dead matter on the live rock if it wasn't properly cured before being sold to you (depends on the age of the live rock). It can come from bad water, or RODI units needing to replace their filters, overfeeding (if you are feeding the tank), ammonia (if you were still dosing the tank), and certain supplements.
If you aren't adding any inputs into your tank, I would perform another large water change. If that doesn't bring it down so that your test kit can register the change, I would look at the possibility of either bad kit reagents, user error in performing the test, or the possibility your rock contains dead and decaying material.
I would not look into carbon dosing at this time. It will cause more problems than solutions.