Good evening Ian,
I'm cautious when it comes to interfering in biological processes with insufficient knowledge of the possible outcomes. I don't doubt that hybridisation of grey duck/pacific black duck with mallards has reduced populations of the former, but I'm uncertain that we have enough evidence to show imminent extinction. That's why I would rather support ongoing monitoring than culling.
I lack the knowledge to comment usefully on the biology, but did find an article that applies.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4947151/Notably, the authors conclude that "halting the introduction of hybridization‐prone exotics and restoring mature and diverse habitats that are resistant to hybrid establishment should be management priorities." However, they also note that "hybridization may rescue the viability of small, inbred populations. Understanding the factors that contribute to destructive versus constructive outcomes of hybridization is key to managing conservation concerns."
On a personal level, the ducks I lump as "mallards" when birdwatching are among my favorite birds and I suspect non-birdwatchers with young children would agree. I have seen ducks that tick all the boxes for Grey Duck in a suburban Auckland pond and also, more commonly in the Taupo region, even decades after the mallard introductions, so I suspect there is a stable remnant population.
The hybrid "vigor" I mentioned in previous post is not an opinion based on specialist knowledge - more an emotive defense of the hybrids as survivors in climate associated environmental change, due to their genetic variability.
Best wishes, Jim