This area used to have tons of Whip-poor-wills, but they are all gone. Haven’t heard one in years and years. They nest on the forest floor, so I think replacement whip-poor-wills released into the wild would just be more prey for the cats if the cats population isn’t decreased. I think the feral cats and owned cats that are allowed to roam killed them all off.
Freegards
Both the eastern and Mexican whip-poor-wills are still so common as to merit a “least concern” rating for their species. So the problem seems to be a local one.
The best bet is a feral cat sterilization and release program sponsored in the local area. They typically take a few species generations to have impact, but it eliminates the vast majority of feral cats. The remaining domestics have a more limited hunting range, so a Whip-poor-will breed and release program would have maximum effect.
However, reducing the feral population could still result in far more mice and rats in the area.