Fair question and aptly put too.
To start, the 6 out of 12 months rule (also called the 'spent leave' rule) is a *constructive* rule. As such, it is meant to be used by IO's as decision criteria for determing whether or not someone should be allowed to enter the UK.
The only time you see it referenced is as decision-making criteria for entry at port or as decision criteria for extension of leave to remain. It is used to help the IO decide what to do when somebody appears at immigration control. If the IO wants to use the rule to construct a rationale for refusing entry, he can do so because that's what the rule is for. Also, if he decides that the rule does not apply or is otherwise not appropriate for that person's circumstances, he can ignore it because he doesn't have to invoke the rule if he doesn't want to. That's why it's called a constructive rule.
Next. The 6 out of 12 months rule, because it's a constructive rule to support decision-making, has nothing to do with overstaying. Overstaying has to do with remaining in the UK beyond the expiry of one's visa. And if your visa says you are good until February, then that's that.
It is often depicted on the internet that if a person is here for more than 6 months out of 12 that they are violating the law. But in reality, they are violating the law only if they have breached the terms of their visa. And in reality, there are gazillions of people whose cumulative time adds up to more than 6 months for legitimate reasons. And can you imagine the chaos that would result if well-intentioned and law-abiding people were suddenly switched to overstayer status despite the fact that their passport showed otherwise? It would be lunacy.
I hope that explains the difference. On to your specific question...
Single women, travelling alone, with "deer in the headlights" eyes, under-financed, and without a credible purpose for being in the UK are basically asking for trouble. And if the IO's radar goes ding-ding-ding, then he will pull the spent-leave rule out of the hat. Why? Because he can do that, and the only way you can argue with it is to have a really good reason for being in the UK. While I hate to say it, there's also the legacy left by American women who came through immigration before you And essentially lied - and that legacy certainly doesn't help. So if he decides to invoke the rule, you are stuffed.
On the other hand, if he lets you in, then you are good to the expiry date. And it doesn't matter if you simply took the ferry to Calais and came straight back and applied for entry. If he stamps you in, you are good. You can spin the roulette wheel like that as many times as you want. If you loose, you'll need an entry clearance thereafter.
And to the difference between you and the OP, the OP is travelling on sabbatical with his wife so he's got a credible excuse for coming and going during his sabbatical, he's got financial resources, probably a thoughtful itinerary, and it would be quite astonishing if the IO invoked the spent-leave rule.
And your final question: is there a way to avoid being held up? I had posted a FAQ tip here in May or June about getting an entry clearance in the USA before you travel. That nips immigration problems in the bud. BAM gone. And yeah, I have an array of tactics, various ports, various schedules and what-not but they can never be posted because it might be misinterpreted as advice on circumventing immigration control. So the best all-around advice if you are worried about it is to get an entry clearance.