Might Sound stupid but...
Ai the inlet remove washer/screen, reverse it, attach winterize hose, insert into antifreeze..presto. When done make sure to put washer/ screen back to original position.
The screen will push check valve open.
Our trailer is a bit more complicate to get the pink stuff down. So I use 1 gallon each for the kitchen sink toilet and bathtub. I have camping world clean it out. Plus they do other maintenance work as well. Good luck. There are some great videos on you tube to help with this.