First, I am unsure about what your regualr water schedule is. How often and how much water do to normally change.
The real question is why is the KH dropping? In a tank there are a few things that use the carbonates/bicarbonates whoch pretty much constitute KH. Some live plants can do this, but you do not have any.
The next thing that can burn though KH is the cycle. The bacteria need inorganic carbon and they can get this from cabonates/bicarbonates. The cycle itself is acidic. This is one of the big contributors to "old tank syndrome."
(Note: All quotes below are from
https://fins.actwin.com/mirror/begin-chem.html#altering )
the nitrogen cycle produces nitric acid (nitrate). Without buffering, your tank's pH would drop over time (a bad thing).
So, if you are well stocked and need a lot of bio-filtration, you have a lot of bacteria using up a lot of carbonates. One way to know what is going on is to test the pH
I am not a fan of water pillows:
Typical home water softeners soften water using a technique known as ``ion exchange''. That is, they remove calcium and magnesium ions by replacing them with sodium ions. Although this does technically make water softer, most fish won't notice the difference. That is, fish that prefer soft water don't like sodium either, and for them such water softeners don't help at all. Thus, home water softeners are not an appropriate way to soften water for aquarium use.
Fish stores also market ``water softening pillows''. They use the same ion-exchange principle. One ``recharges'' the pillow by soaking it in a salt water solution, then places it in the tank where the sodium ions are released into the water and replaced by calcium and magnesium ions. After a few hours or days, the pillow (along with the calcium and magnesium) are removed, and the pillow recharged. The pillows sold in stores are too small to work well in practice, and shouldn't be used for the same reason cited above.
Not all water softeners use salt. However, the alternative to a salt based softener is mostly designed to prevent calcium buildup in pipes. A salt-free system works by crystallizing calcium, but not removing it. So you need to know which system you have before you start ysing Sodium bicarb. If your softener is adding sodium, you need to be careful about adding more.
Here is the info on using both calcium carbonate and sodium bicarbonate (baking soda):
Hardening Your Water (Raising GH and/or KH)
The following measurements are approximate; use a test kit to verify you've achieved the intended results. Note that if your water is extremely soft to begin with (1 degree KH or less), you may get a drastic change in pH as the buffer is added.
To raise both GH and KH simultaneously, add calcium carbonate (CaCO3). 1/2 teaspoon per 100 liters of water will increase both the KH and GH by about 1-2 dH. Alternatively, add some sea shells, coral, limestone, marble chips, etc. to your filter.
To raise the KH without raising the GH, add sodium bicarbonate (NaHCO3), commonly known as baking soda. 1/2 teaspoon per 100 Liters raises the KH by about 1 dH. Sodium bicarbonate drives the pH towards an equilibrium value of 8.2.
(100L =26.42 gal.)
When I did my high tech planted tank and was adding pressurized co2 I worried about a pH crash caused by the the acid from the co2 using up the KH. I did not want to raise my GH. so I used a small amount of crushed coral in a bag in my filter. It amounted to about 1/2 cup for around 30-36 gals of water. It dissolves over time and needs to be repelenished. A small amount did not moe my GH. This works a bit slowly at first and then should level off. When things start to slide backwards its likely time to replenish the coral.
Finally. the conversion factor from KH or GH dg to ppm is about 17.8. This means that when you read 9 dg (drops) for KH, your ppm is at least 143 and a max of 177 ppm. ( 8 dg 17.8 x 8 =142.4 and 9 dg = 160.2, but if your KH is say 155 ppm that is over 142.4 but under 160.2. So it should still read as 8 dg. I cannot say this is factually correct because i do not know how accurate the KH test kit is in terms of ppms nor where the brak points are for each added dg.)
Here is what I suggest you do. When it is time for the next regular wc, test both KH and GH. The do the change and test again in about 15 minutes which gives the water time to circulate and mix. You know you are using up KH, but what about GH? If it is dropping some between changes, then you may not need to worry about them raising the GH much if at all.
Finally, pretty much any tank which does not have any live plants should almost never have 0 nitrate. This is also the worst or all the tests we use. The nature of the reagents, especially in bottle #2, is that they precipitate out of solution. This means they becomes solids, sink to the bottom of the bottle and stay there. They need to be mixed back in. Doing this means shaking the bottle hard, then banging the bottom on the table a few time and shaking it hard again. Also shake bottle #1 well but it is not as bad no banging the bottom is needed. Measuring nitrate is problematic in general. the API kit works by converting it nitrite and then measuring that. It is considered to be least accurate between 0 and 20 ppm. That does not mean it is not a useful test. But you must be sure to do the above to bottle #2.
So I am not sure your nitrate results are accurate. Just in case, also please check the expiration dates on your test kits. They should be fine but let's be sure.