Bung popped off, I tied it down

You'd probably be better off with blow-off tube. That aside, it is unlikely that the pressure will damage your carboy...but you may have a mess on your hands if the krausen goes up and through your air-lock.

 

Given what you described about the ingredients of this beer I agree with JohnSnowNW that you need a blow off tube, and the quicker the better. Those 3-piece airlocks are notorious for clogging at the tip once the krausen rises to that level, and you'll have enough pressure build up that it is capable of blowing off the top of a fermenting bucket. Cram a 3' tube into the bung hole in place of the airlock and stick the other end of the tubing into a bucket of water sitting next to your carboy. I use a plastic tube that is the same outer diameter as the mouth of the carboy, so there is no chance of the bubbles clogging up that tube. If you want to keep your airlock in place, cut the 'crosshairs' off the tip inside the carboy, remove the inverted plastic cup and attach your tubing directly to the stem.

Edit: What ambient temp is this beer at? You're in Texas so you may be making your yeast too happy if they are too warm.

 

Your yeast are happy. If Mt Vesuvius erupts it'll happen while you're asleep because those little fellows have a perverted sense of humor . . . and they don't have to mop the floor. Search Google Images for "blow off tube" and you'll see how to do it. I would not leave it overnight with the airlock tied down. I sleep better knowing Mr. B. O. Tube is on duty. Once the blow-off stops you're safe to go back to an airlock.

 

You'll still want to watch that your tube does not get clogged because it is only a quarter-inch inner diameter, but you're a lot safer now. I don't know of any reason that you can't use a blow off tube exclusively, although it can be a bit more cumbersome if you have to move your carboy for any reason.

As for your comment about racking to a secondary, there is no need to do that unless you are going to soak the beer on fruit, oak chips, or age the beer for an extended period, you should skip using a secondary.

 

Is there any way that you can get it to a slightly cooler location and keep it fairly stable? You've got a fairly big beer that will generate additional heat from the fermentation process, so you're pushing the upper limit of getting it too warm and risk getting off flavors. Just putting your carboy on the floor instead of a table can possibly get you down a degree or two. The closer that you can get your carboy's location to 65 degrees, then the better off you'll be.

 

The more frequent that you can dampen that towel, you'll get a lower temp from the evaporative effect. The towel should be wrapped around as much of the carboy that it will cover.

Getting the beer off of the trub can be another reason for using a secondary, but unless you are not able to package your beer within a month from now, I wouldn't worry about it. Just use extra care when you siphon to leave as much behind that you can.

 

Keep in mind that yeast don't watch a calendar, so the beer will be done when they are done. Two weeks is typical but you've got a big beer here, and the time period to ferment will depend on your yeast pitch rate and how happy they are. Sometimes those little critters are hard to predict. Extra time in the fermentor will also allow them extra time to try to clean up behind themselves. You easily could be approaching a month before you can package your beer. Just baby sit it for now and see how things go.

 

Recipes are notorious for using 'two weeks' as a fermentation period, and probably 75% of beers are done in that period, but different circumstances (fermentation temp, yeast selection, OG, etc.) create different fermentation speeds.

The hydrometer is the most sure way to know, and after two weeks is usually a safe period to check the gravity (assuming you are not seeing obvious indications that fermentation is still ongoing, like bubbles in the airlock). If you get the same reading a few days apart, and your readings are close to the expected gravity, then you are done. Any extra time that you can give the yeast to clean up after themselves before packaging will be a bonus to the quality of your beer.

 

Here's the science of what's going on in your primary:
http://www.morebeer.com/articles/conditioning

As stated by the Matriarch Water Fowl, the yeast have their own way of dealing with things. You're learning they are the masters of the brewhouse . . . you are the slave.

 

I say you're golden.

One thing I'd like to comment on, is that if that bung you're using is silicone (hard to tell from the pic)...do not use that if you ever do an extended secondary. Silicone is the most oxygen permeable material we generally use in homebrewing.

Good Luck!