The winterizing valve is what keeps the city water pressure from the winterizing port. I completely removed the check valve from my winterizing port; no issues.
I think my main problem getting the pump to prime from the winterizing port was a poor seal between the port and the hose going to the anti freeze jug. I need to work on this some more; I've had problems every time. I may install a winterizing kit like my last trailer had (no winterizing port); it has permanent connections to an intake line; never had a problem with it.
https://www.amazon.com/Camco-Permane...e+rv+kit&psc=1
Attached is a drawing of my convenience center plumbing; your plumbing may not be the same.
__________________
Scott & Alta
2017 Montana 3160RL, Legacy, Onan 5.5Kw, Solar
2022 F-450 Lariat Ultimate