I go back to the States for a few months and return for another 6 months?
The basic answer to your question is yes.
There is no limit on the number of visits a person can make to the UK, and there is no requirement that a specific period of time must elapse between visits. The basic rules assume that when a visitor leaves the UK, their LLR is voided. When they return, they need a brand new LLR.
To balance that statement, the IDI's contain a constructive rule that says a person's time in the UK as a visitor normally should not exceed 6 months out of any year. If an IO does not believe your intent on visiting the UK, they can use this rule to prevent you from entering.
Do people leave the UK and then come back in? Yes. It's quite common.
Is that legal? Yes.
Do people go out and come back and get refused entry? Yes, that happens a lot.
Do people go out and come back and get a reduced LLR? Yes, but it's less common.
If a visitor comes to the UK and stays for 4 months, goes to France, and returns and is given another entry stamp and then stays for another 4 months, it means they will have stayed in the UK for 8 months. Are they an overstayer? No. An overstayer is someone who has stayed beyond the end date of their leave. The end date of their leave is stamped in their passport each time they enter. A person can't really overstay if their LLR is still unspent.
Is it all truly down to whether or not the IO is in a good mood? I know it looks that way sometimes, and there probably is a small element of chance involved. *BUT* reading the statistics and profiles, what you get is that they are astonishingly consistent. And the notion that everything is based upon luck underestimates how the Immigration Service works. Based upon that, there's no excuse for not being prepared with the stuff Lola mentioned above. And if you're still worried, then get an entry clearance.