Say, a thread in GQ gets too political and is sent to GD. If the tone grows harsh, can it be moved again to the BBQ Pit? Or if the tone grows factual again, can it be moved back into GQ?
Yes.
Absolutely. Only the great respect they have for each other prevents the Mods. from making any given thread into a game of volleyball – “Here, you deal with this!” “I don’t want it; here, catch, it’s coming back to you!” “#%@#@, I sent it to you, now keep it!” and so on. 
The mods are physically able to move the threads at will. It takes a modicum of effort, and some minor bandwidth.
They do tend to avoid excessive forum changes, because it takes their time as well as bandwidth to move them, plus it gets confusing to folks trying to follow the threads. Generally, once a thread moves to GD or to the Pit, it will stay in that forum. If the content of the thread was enough to deserve that forum, then even if the tone lightens or whatnot, that content is still there.
There’s a current thread that went from CCC to IMHO to the Pit. (It was pure idiocy, not worth a link).
But once things get to the Pit, they tend to stay there. Not to say it’s never happened, but I’ve never seen a thread moved from the Pit.
The mods do also keep a tally of who owes whom beers for moved threads. As I recall, Czarcasm and TVeblen have a whole drunken orgy coming to them on my behalf, as soon as we ever should meet, for all of the threads I dumped onto them. I don’t even want to think about manhattan’s tab to them.
Question answered. Also, a short time after I posted it, I saw a thread go from GD to IMHO to the Pit.
Someday I’d like to see a thread get moved to every single forum.
I actually wanted to introduce that as a game once. I was going to call it the “Around the World Thread”. (The SDMB is my world).
There were 2 variations: one where I announced my intentions in the OP, the other where I didn’t. For the latter version I figured once I accomplished the task I would reveal my sneaky plan and we all, posters and mods alike, would have a good laugh over it.
Soon after, I envisioned a more realistic scenario where I was surrounded by mods staring at me much in the way the wizard looked at Mickey Mouse in Fantasia after Mickey flooded the place.
I decided some games are better left unplayed.