As a vegetarian I also wonder why your 'western' diets have to be so meat centered. Like the meat is the center of your dish and everything else just compliments and supports.
Why not have western diets which are less meat focused, and instead use meat as a garnish. In history, particularly in regions like Egypt, the Levant, Persia and the Indian subcontinent, raising animals for meat was considered an extreme indulgence rather than something everybody would do. Our recipes are far more vegetable and bread based. Meats, when they are consumed, are used as a garnish to add flavor. So its kind of rare for people to eat huge steaks and racks of smoked ribs. I understand nomadic hunter-gatherer tribes in Northern Europe and the Americas had a much more meat centered diet because animals were plenty and probably easier to hunt. But people must have foraged for nuts, berries and herbs too. Even if just to add seasoning and marinade for their hunted meats.
Perhaps this is where the western idea of meat focused dishes arose? and because Europeans colonized the Americas in our timeline, the idea kind of stuck and caught on because there were already nomadic hunting tribes with meat rich diets in the plains of North America?
If another region had colonized the Americas instead, say India, Persia or Egypt, or even a surviving Al-Andalus, do you think western diets would be less meat focused and be more vegetable and bread based instead? Or instead maybe the nomadic hunter-gatherer tribes of Europe and north America develop agriculture and learn farming early instead of foraging and hunting?
I don't know about that. Obviously pre-modern western diets had less meat since that was before factory farming of animals. But American Indians generally had to supplement their diets with hunting for various reasons (agricultural peoples in Eastern North America), in addition to those who were entirely hunter-gatherers (Plains Indians, West Coast Indians, etc.). It's interesting that meat-rich dishes like Southern-styled barbecues and South American asado are New World in origin, but the fact that those nations are so rich in agricultural land used for cattle ranching is part of the reason.
You have Egypt, Persia, India, etc. colonising the New World, they'll still have a large availability in ranching land and in general, a lesser population density allowing for more livestock. India at least has Dharmic religions and their vegetarian tendencies, but I think their experiences on the frontier would challenge that mentality so that you've have far less vegetarians amongst those Indic New Worlders.
For North American Indians, the best chance for less hunting and meat in their diets is for the Eastern Agricultural Complex to not be abandoned in favour of maize and other Mesoamerican crops.
I first had goat several years ago, in an Indian restaurant; I rather liked it.
Everytime I had goat at an Indian restaurant, it had bones in it you had pick around. Certainly you can have more "bone-out" goat meat sold. And I reiterate my previous point about how rare goat meat is despite the large variety of goat breeds and indeed, goat flocks, in Western countries.
While rabbit is tasty and cheap to grow, the meat is too lean to make it a staple food (google search "rabbit starvation"). That being said, wild cows are a lot different from domestic cows... maybe a concerted breeding program could have produced plumper rabbits which would be healthier for human consumption and make up a larger part of the western diet.
Maybe in the past, but nowadays with such a health-focused society, rabbit could (and IMO should) rise in popularity since it's a cheap, lean, and healthy meat. The concept of rabbit starvation has uses for weight loss.
Fatten racoons and possums and possums on fruit, get them younger and keep the confined. Don't eat them if they are older and especially breeding males
I believe in many parts of the US, it's illegal to keep those animals in captivity (for pets or livestock). Gotta change the laws to get them integrated into cuisine. A lot of people shy away from them because they're such a common source of rabies. Which you can hunt them or pick them up as roadkill (legal to process roadkilled animals in many states), but they have a stereotype of disease surrounding them (they're dirty pests for one) that makes it hard to ever make a market.
I agree they would make good livestock (it's classic Southern US cuisine), but there's still the laws surrounding keeping them to overcome. Speaking of roadkill pests, there seems to be a market for armadillo I've seen, so perhaps it isn't entirely hopeless. Florida's gator cuisine (my Grandpa describes gator as like chicken but with a "metallic reptilian tinge" to it, which I'd completely agree from my experiences with it) is a good model to follow to get possum and raccoon served more widely.
Since I mentioned gators, what if they became more popular in general? Crocodile/alligator skin is a popular leather, so why not the meat of the animals too?