You can get substrates that don't leach ammonia - I think JBL AquaBasis is one. Either way that's going to be a pretty major change so I wouldn't do it with the fish in. It's going to make a big mess. You want some big buckets/storage boxes. Remove the fish and plants into them, clear out the current substrate and replace it, replant plants, let it settle and re-add the fish. Keep the filters running on the fishes storage buckets whilst you do it.
If you really want to use the ADA stuff, I would look at setting up somewhere else for your fish for a month or so to let the ammonia spike clear. Adding substrate a little at a time will make a big mess, take ages and still risk effecting the fish. Pick up a second hand aquarium or use a couple of big storage boxes as temporary holding tanks.