Hi Astroboy, greetings from central Kentucky.
Congratulations on your new AS acquisition, may you have many carefree miles of adventures ahead of you.
The suggestion of using a bag of ice in your black tank has been disproven. The dish soap is good but the cubes just bang around in there, floating in the water and not doing much good. Look for some videos on YouTube for some tests.
We have used tablets, powders and liquids in both the gray and black tanks. Our experience has been that the gray tank smells as bad as the black, sometimes. We mix up the stuff according to directions and then put it in the toilet or the vanity sink, closest to the gray tank. Before we leave a campground (especially headed home) I have 6 gallons of tap water in some left over gallon water bottles. We flush the black, close, dump in 4 gallon bottles, open the black valve and it is usually running clear. (I have an elbow on my slinky that is transparent.)
We do the same to the gray, close the black, dump the gray, close the gray, then put a gallon down kitchen and vanity sinks and dump again. That runs pretty clear also.
If we are leaving and heading for another campground a hundred miles or more away, we put a treatment in the black tank ( we use Extreme Tank Cleaner:
https://www.amazon.com/gp/product/B0...?ie=UTF8&psc=1) let it slosh around, then dump on arrival at the next site. That has made a big difference for us.
Happy trails