If the appearance of ich on your fish is gone, it is too soon to stop the treatments. The treatments need to continue for several days after all signs are gone. I try to give it a full week of treatment after. If you put the carbon back in right away, get it back out and finish the extra week of treatment. After that you can use carbon to remove the medication that you are using.
80% water changes, by themselves, will slightly reduce the number of obvious parasites on the fish but will not make the tank free of the parasites. They will re-infest the fish in a fairly short time. You need to actually treat the tank long enough to kill all of the free swimming parasites after they fall off the fish. That takes a few days.
If you remove your other filter media, you will destroy whatever amount of cycling that you have already accomplished, so don't do it.