I'd get one of these: https://www.amazon.com/Valterra-A01-0187VP-Flexible-Tank-Wand/dp/B000BGHYE8/
Flush with the tank open, and as others have said, you'll need to fill it some and let it sit between flushes to soften things.
If you don't have one already, there are clear sewer connectors that will help see what's coming out while flushing.
We have one of the wands below. I've never had a clog that it couldn't break loose, and I use it as my main tank flush every month or so.