"In recent weeks, so many people have called Bill Crain’s Hudson Valley farm rescue to surrender their ducks and chickens — many purchased at the height of the pandemic lockdown..."

"... that he finally marched into a local farm store and demanded to speak to a manager. His plea: Stop selling chicks and ducklings.... 'It’s a crisis that people are abandoning these animals,' he said. One of the slim silver linings of the pandemic’s earliest days was the addition of animals to many families. Some people, decamping from virus-besieged cities for the countryside, stoked a craze for backyard fowl.... Socially distant and lonely, or with kids to entertain, many cleared pet store shelves of gerbils and lizards, chinchillas and snakes....Why families are holding onto cats and dogs but relinquishing smaller animals like guinea pigs may have to do with human attachment, several experts said. On Staten Island, Jade said she was able to bear parting with her guinea pig because Honey was less interactive than her dog and cats. 'They look adorable, but I think people have this misguided conception they are going to be able to provide this companionship and fill a void that the are looking for,' said Allie Taylor, the president of Voters for Animal Rights.... On Wednesday, a box containing 22 guinea pigs of all ages was found abandoned in the lobby of a Staten Island apartment building...."

From "The Great Guinea Pig Giveaway Has Begun/From geckos to chinchillas, small pets were a pandemic balm. Now shelters across the country say they are being surrendered" (NYT).

The solution is, clearly, to eat these animals. You don't need a rescue sanctuary. You need meat processors. Ducks and chickens are obviously edible. Eat them, and the problem is gone.

But what about the guinea pigs? What about them?! Look it up. They're especially good. They've even — like pigs/pork and cattle/beef — got their own name when they are converted into meat: cuy (or cavy).

Here's a Modern Farmer article, "Is America Ready for Farm-to-Table Guinea Pig? The ubiquitous kids' starter pet / lab animal could soon be raised at a farm near you":

Several mom-and-pop eateries in Queens serve guinea pig once or twice week. The owner of Sabor Latino in Elmhurst, Jesus Inga, says he would like to serve cuy but that only very small restaurants can get away with doing so. He fears getting in trouble with local law enforcement.... But, serving guinea pig is actually legal. 

Under federal law, it’s considered an exotic meat.... Some restaurants in Los Angeles, California, another pocket of heavy South American immigration, are serving cuy as well. Although California law prevents any person from selling, buying, giving away, or accepting “any carcass of any animal traditionally or commonly kept as a pet or companion with the intent of using or having another person use any part of that carcass for food,” the law seems yet to be tested when it comes to guinea pig. 

Not all restaurants have an immigrant crowd to please. And that begs the question if there is a market for raising guinea pigs outside of the South American community. For Peter Platt, one of the family owners of Andina, a popular Peruvian restaurant in Portland, Oregon, the answer is a resounding yes: “Portland is a foodie town and has made a name for itself nationally as a very vibrant indie restaurant scene,” he says. “Consequently our local customer base prides itself on being adventurous and trying new ethnic cuisines.”

Yes, let your foodie pride flag wave. Eat the cuy. 

ADDED: Actually, I wouldn't want to eat meat that was raised by some random pet-surrenderer. There 2 distinct problems. First, once an animal is a pet, it is imbued with something like humanity that makes us feel at least squeamish, but maybe even morally outraged. Second, meat raised by some random private citizen might not be wholesome. Who knows what it was fed, what drugs it took, what lead paint chips and other detritus it nibbled? 

AND: Here's an NPR article from 2013, "From Pets To Plates: Why More People Are Eating Guinea Pigs" by Alastair Bland. (I love that name, Alastair Bland!) In classic NPR style, we're told we ought to eat guinea pigs out of political rectitude:

According to activists, eating guinea pig is good for the environment. Matt Miller, an Idaho-based science writer with The Nature Conservancy, says rodents and other small livestock represent a low-impact meat alternative to carbon-costly beef....

To render a pound of meat, a cow, he explains, may require 8 pounds of feed. A guinea pig only needs 4.... 

"There's a clear cultural prejudice against eating guinea pigs, and rodents in general, in the United States," Miller says. "But finding ways to reduce our carbon footprint is a good idea, and so is eating small livestock, like guinea pigs."