The problem is, the mass produced chicken most of us are used to doesn't taste like chicken.
The expression 'tastes like chicken' is therefore used for most anything that's not particularly assertive.
There was an episode of Food Detectives, "Tastes Like Chicken" where they served a few different meats to professional chefs (Alex Guarnaschelli and Aarón Sanchez), who had problems identifying all of the meats they were being served ... I can't remember exactly what all of the results were, and I can't find a transcript; I remember Alex being distraught when she realized she was eating guinea pig).
And the cooking show Ham on the Street had a regular segment of 'name that meat', where he'd have hot dogs, or jerky, and try to have people guess what they were.
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Part of the issue with substitution is going to be something that has similar cooking characteristics, but that you don't have a reaction to. (I'm actually surprised that you're allergic to chicken, but then listed other poultry)
Turkey's likely the closest of the stuff you listed, particularly if it's the mass produced stuff, it's going to have a similar lack of flavor that most chickens sold in the US has; duck tends to be richer. I haven't had any game birds recently, so can't comment on the pheasant. Alligator I've only had a few times, and the only time in the last decade it was deep fried, so the meat didn't come through.
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For substitutions, it'd depend on how you're cooking it, and what part of the bird.
For instance, in place of chicken wings, I might consider frog legs. (although, it's probably been 25 years since I've had 'em, but I seem to recall them being chicken-like ... I just can't remember if they were like white or dark meat chicken) ... but they'd be closer in mass than turkey wings.
For chicken breasts, I'd go with turkey breast cutlets, so they're closer in size. For ground chicken meat, ground turkey will work, just check to see if a recipe calls for a leaner or fattier mix, and get the appropriate turkey. Chicken thighs and legs are a little more strongly flavored ... rabbit might actually work, or duck or pigeon if you have a source.
An answer to your edited points.
Number 4. Pores don't do much during cooking. It is about cell walls and proteins. A pore is a channel constructed from zillions of cells (like a tunnel constructed from bricks). A cell is like a bubble (the cell wall) filled with liquid (the cell plasma). The cell wall is made from zillions of proteins, like a hat knitted from wool. In freezing, the plasma turns to sharp ice crystals and tears the cell walls apart (like poking holes in a hat).
Then under heat, the proteins unravel the way you could unravel a knitted hat if you tugged at it. If you cook the meat just a little, the proteins remain bushy and soak up liquid. If you overcook it, they stretch and start looking like a long, smooth thread and can't soak up water and/or cell plasma any more. The meat tastes dry and unpleasant.
Freezing the meat is just bursting the cell walls. Unravelling the proteins is denaturation. They are two different things.
Number 1. More water does indeed mean more damage to the cell walls. No denaturation happens there, as explained above. But you can't change the amount of water within the chicken cells in any way while it lives. This amount self-regulates, like blood pressure. If you feed the chicken more water, it will excrete more water, not store it in its cells.
Number 2. You want lots of air around the chicken if you want to get ice crystals buildup on its surface. That's why Sobachatina suggested an inflated bag - to keep air around it. Also, unpacked chicken will make your freezer dirty and contaminate other food with uncooked meat juices, which is dangerous.
Number 3. As far as I know, water ice expands while cooling from 0 to -4°C and then starts shrinking. Most damage is done while the crystals expand, so I suppose that most of the damage will be completed within the first 1-2 days (depending on how long it takes for the complete chicken to cool to -4°C).
Best Answer
Yes, there is a clear difference in never-frozen vs. defrosted meat.
The cell plasma in your chicken freezes in the freezer, turning into ice crystals. Since cell plasma is over 90% water, it expands instead of shrinking in the 0 to -4°C range. The crystals cut the cell walls. When you defrost the meat and cook it, the cell plasma flows out into the pan, leaving you with dried out meat. This is the first, major problem with freezing, and occurs even when the meat is frozen for a very short time.
If you keep meat stored frozen for longer time, there are two other effects. The unavoidable one is rancidity. The cell plasma in frozen meat has a high mineral concentration, and given time, it will oxidize the fat in meat, changing its taste for the worse. The avoidable one is freezer burn - it occurs if the meat is not wrapped properly in the freezer. Freezer-burned meat is really unpleasant to eat, most people throw out affected parts.
Of course, this is not the only factor affecting meat quality. SAJ14SAJ's comment is true in the sense that bad meat (from mass-produced young animals grown in bad conditions) will not have much taste of its own, and even if you prevent it from drying out, it still won't be as nice as good meat. But what is more pertinent in this case is that the cooking process can more impact on drying out than a freezing-defrosting cycle. If you cook defrosted meat carefully, you will minimize the dryness effect. It won't be the perfect morsel, but it can still taste pretty well. On the other hand, if you have never-frozen meat and overcook it, it can get to shoe-leather consistency, so that you lose all advantages from non-freezing.
References: McGee on Food and Cooking, p.146 (reputable, dead-paper book) or http://www.wedlinydomowe.com/sausage-making/freezing-meat - (random Google hit, one click away).