My (probable) solution:
1. Add bag with crushed coral instead of relying on buffer
2. Remove Purigen to allow more good bacteria to form
3. Temporarily remove fine sponge to allow for better water circulation
4. Stop dosing Ammolock, continue with StressZyme dosing
1) Good. Do this. Keep adding buffer, too. Coral is slow reacting.
2) Good. Do this. You do not want the bacteria to colonize the Purigen.
3) Good. You could put a coarse bit of sponge over the filter. This sponge will get colonized, too.
4) Use a simple dechlorinator. It does not matter if the ammonia is locked up. The bacteria can use it. Do not use Stress Zyme. This produce may have some value when the fish have been handled, but has absolutely no value in cycling a tank. Do not use anything that adds slime coat to the fish.
What is removing the carbonates? Some substrates will do this. I would suggest adding baking soda (Works for me) but if you do not want to add that much sodium then look for potassium bicarbonate.
White stuff at the water line is often minerals.
White stuff under the water might be other things. Can you describe it better?
Flaky, granular, stringy, gooey, gritty, individual particles? (What size?) a film?
Here are some possibilities:
Reaction between 2 or more things you are adding to the tank.
Test: Put some water in each of several jars and add each additive separately. This will show if the white stuff is a reaction between the water and some additive. Then add each additive to the jars of water in pairs. See what different combinations will do.
Often pH altering things will cloud the water, less often will precipitate.
Some fertilizers are incompatible: Phosphate and iron fertilizers should not be dosed together.
Something settling out through the water. Is there anything in the house that might be doing that? Is the dust in NY white?
Maybe some slime from the slime coat additive. Some of these materials irritate the fish into creating excess slime coat, but others actually contain some kind of gel (Aloe is often listed) that can settle out.