Sounds to me like bad shallots. If shallots taste anywhere near as pungent as onions, then they're of low quality and shouldn't be used (at least not in anything raw or delicate). Always taste shallots before use.
You may also be particularly sensitive to some of the shallot's flavors. There's nothing wrong with using less in your vinaigrette. It's there not just for flavor, but for its emulsifying compounds. All members of the allium family have these; you can use garlic or scallions or chives and all will help make an emulsion. They all work in very small quantities.
The other suggestion is that maybe you don't like shallots at all. You can use something else. If not a different allium, then there's mustard (the most traditional), egg yolk (the Caesar's solution), or tomato paste. I've used mango chutney (it's got cooked onion and who-knows-what-else).
Re: the Cook's Illustrated solution, I'd be very wary. I've never heard of a chef doing this, even at the most cutting edge restaurants. It seems like a solution in search of a problem. I've found the palates of this magazine's testers to be extremely unreliable over the years. Caveat emptor.