Putting hormesis to work to counter depression sounds to me like a great idea. If your wife is willing to experiment, you might be able to be of great service to her. Here are some thoughts on how you might go about it. I'm no expert; I'm just speculating and hoping this will lead to something fruitful.
1. Look for clues to regulatory feedback loops.
I don't think this is right: "Depression seems to result from a mess of negative thinking patterns, as well as an extreme sensitivity to any and every negative event, and an extraordinary propensity to take everything the wrong way." Rather, depression is those things, and results from other things, which are not well-understood. Or better still, depression is a state where your emotional "set point" is set very low. Really, "depression" is a pretty vague term. The feedback loops that are active during depression probably include a lot more than just thought patterns and sensitivity that maintain a feeling of hopelessness. Depression also commonly involves changes in sleep patterns and in appetite. For example, when some people are depressed, they sleep a lot more than normal; others sleep less. Often when people are depressed, their appetite reduces and focuses mainly on starch, and they gain weight if try to eat their usual diet.
That all suggests that depression is a disorder of many simultaneous feedback loops in the body and brain (a "regulatory disorder"), mutually reinforcing each other and keeping the whole person in a bad "basin of attraction". Or rather, "depression" probably covers a variety of different kinds of bad, mutually reinforcing feedback loops. And that, of course, suggests that hormesis probably has something to offer.
So, one course of action you and your wife could start off with is to look for non-mental correlates of her depressions. Do they tend to happen at certain times of the year? Do her sleep patterns change? Does she crave a certain kind of food?
I've heard that people living at arctic latitudes often get depressed during the *summer*, when the days are extremely long, because their circadian rhythms stop getting entrained by the Sun. (They don't see enough "dark" to trigger the rest cycle, so they start tuning out "light" and don't get triggered for activity, and it spirals out of control.) For some people, the main trigger for depression is the high *rate of change* of the length of the day around the Spring and Fall equinoxes. If you find a correlation with time of year or sleep schedule, that suggests that a simple cure is to help stabilize your wife's sleep schedule, especially during prone times of the year. "Light therapy" has been helpful for some, and has received some serious research. What time you eat as well as what time you wake can also have a lot of effect on circadian rhythms. Basically, the trick here is to knock the system out of a bad attractor basin and into a good one, so your wife's whole body tends to keep her in her normal state. Sometimes, just staying up all night can knock someone out of a depression.
if your wife craves a certain food while depressed, that food might itself be the cause of the depression—especially if the food seems to bring some relief. Again, this would be a case of a bad attractor basin, where feeling bad, craving the food, and eating the food are themselves part of the self-stabilizing feedback loop. A simple experiment to try is to cut that food out for a month. If the food is part of the bad feedback loop, she should feel *worse* for the first few days and then come out of it.
2. Paradox psychology
Actually, something I like about hormesis is that it doesn't require you to figure out causal connections in much detail. That's usually not feasible, and even when people figure out key links in the causal chain, those usually just lead people to target a single key link, and thereby set up a new, bad feedback loop where the treatment is itself part of the loop (like craved foods, above).
Paradox psychology is a way to get the system to add a self-correcting feedback loop of its own. The technique is: do the bad symptoms (depressive thoughts, etc.) deliberately. For example, during a depression, *decide* to come up with reasons why your situation is hopeless, to favor negative interpretations of ambiguous events, to feel helpless, etc. Another approach is to schedule the bad thoughts and emotions. For example, you decide that at 8:00 p.m. on Tuesday, you're going to see only negative outcomes for every possible action you're considering in some important part of life. I believe it's supposed to work best if you schedule the depression at a time when you expect it to happen on its own.
After each time doing one of these deliberate depressions, your wife reports whether she succeeded or not. It's a "win/win" situation, since if she "fails", then she's succeeded in overcoming the depression, and if she "succeeds", then she's succeeded in taking control of it.
This is the opposite of the usual "will yourself out of it" advice, which I think is pretty well known not to work. Using willpower directly against your own mood just reinforces whatever feedback loop is producing the mood (which, BTW, can be handy if the mood is positive). Deliberately engaging in the mood sets up whatever additional feedback loops are needed to give the conscious mind control over it. What's actually going on in the brain is probably way too complex to consciously understand or control directly. "Will yourself out of it" puts the entire burden on the existing ability to control mood; "do the unwanted thing deliberately" provides a way for that ability to gradually grow.
I've heard some people report success with merely *monitoring* their mood and making no attempt to oppose it, increase it, schedule it, or anything. For some people, this might be enough to trigger a self-correcting feedback loop.
Naturally, whichever approach your wife tries, it has to be done enough times, over a long-enough period, that there is a real opportunity to get past the initial weirdness and see second-order effects (positive effects that are triggered by the weird/negative first-order effects which you can induce directly). Logging each "treatment" and how things went is probably crucial.