You could use oil, but I don't think it's worth it; realize that you're going to be using additional energy for obtaining, cleaning, and disposal of it.
Regarding using a broth with a porous bag, well, that isn't sous vide. That's more akin to a slow-cooker. The whole point of sous vide is the airtight barrier between food and heat.
Update
Oil does not have a higher thermal mass than water. Ammonia does, but I'd suggest avoiding that. ;)
Source: http://www.engineeringtoolbox.com/specific-heat-fluids-d_151.html
Has anyone had success at large scale sous-vide at home?
My scale was not quite as big as yours, but I cooked my Thanksgiving turkey for the extended family this year sous vide. Not only was the outcome a huge hit among the guests, but it was a huge relief for (your truly) the chef.
I want to go to party scale, say 30 to 40 servings, what are my chances of success?
In my experience, scaling up is one of the biggest advantages of cooking sous vide. Cooking 30-40 servings on a home stove would be a daunting prospect, to say the least. With sous vide, 15–20 servings is only marginally more work than 4–6. Again, I've not done 30–40, but it should scale accordingly.
Should I just get three or four chilly bins or just one large bin?
If your food will fit in one cooler, it will work, but I think you'll find it much easier to use more. The more water you have, the slower it will lose heat, and thus, the less you will have to pay attention to it. I also typically cook chicken and beef at separate temperatures, so I would probably have two coolers for chicken and two for beef.
Best Answer
First, I'll echo Catija's comment and say that there's no major advantage to cooking these breasts together. I know Kenji does it here, but his purported claim toward greater evenness in cooking isn't really something you need to worry about with sous vide. In fact, by creating a thicker piece of meat for your water bath, you're guaranteed to make the cooking less even, since it will take much longer for the interior of the meat to reach water bath temperatures.
So, my first recommendation would be to just cook the two breasts separately, making sure water circulates around both. In that case, you probably don't need to modify your cooking times at all.
But let's assume that you really want to cook your 6-inch cylinder for some reason (perhaps to create a large "meat tube" for slicing if you tie it up well). Okay. Assuming your sous vide setup circulates water well, one advantage of sous vide (in addition to the precise temperature control) is the significantly greater heat transfer from water to food compared to, say, air in an oven.
In practice, that means that even rather large hunks of meat come to temperature a lot quicker than they would in an oven. The main reason to increase time with a larger turkey breast would just be to allow for the center of a large cylinder of meat to rise to the water temperature.
The following recommendation assumes you're going to be using a water bath quite a bit above the "danger zone" border, say at least 140F/60C.**
I played around with a bit of heat transfer modeling here just for kicks, and I'm pretty sure your 6" diameter cylinder wouldn't take that much longer to come to temperature. Allowing the center an extra 30-60 minutes might be reasonable, but that's still well within the parameters of your 2.5-4 hour recommended window. I'd tend toward the longer side of that time span (closer to 4 hours), just to guarantee sufficient time with the center above the "danger zone" limit to kill off bacteria. You obviously could go over 4 hours without compromising safety, but eventually the outer layers of the breast will start getting softer and more mushy (which might be a less desirable texture).
Lastly, for large hunks of meat cooked sous vide for relatively short times, I'd strongly recommend putting in a probe thermometer so you know what the core temperature is and when it gets above the "danger zone." (See this Modernist Cuisine video.) If you don't have a thermometer to leave in, I'd check the temperature with an instant-read thermometer after a couple hours to be sure you're at least getting above 130F/55C.
** Note: Precise sous vide temperatures are CRITICAL here for safety. The closer the center of the cylinder gets to the water bath temperature, the slower its temperature rise becomes. Getting the center up that last 5-10 degrees or so takes a lot longer. I've seen some sous vide turkey breast recommendations with water bath temperatures as low as 132F/56C. In that case, the center of a large cylinder may be skirting the "danger zone" boundary for much of the cook time and might not be safe even after 4 hours in a bath. In that case, you might need to add more cooking time to guarantee safety. Alternatively, you could raise the water bath temperature by a few degrees for the first hour or two, and then lower it to finish cooking. Either way, if you're not sure your breast will spend a significant amount of time near 140F/60C or above, I'd definitely check the core temp mid-cooking and consult sous vide guides to make sure you have enough time above 130F to pasteurize.
Whatever you do, I'd recommend choosing a temperature designed to get the center of your cylinder above 130F/55C within two hours. Sous vide turkey usually isn't heated to the much higher temperatures that people have traditionally used for oven-roasted turkey. Those higher temperatures not only guarantee killing off bacteria (and a drier turkey) but also serve as an additional safety measure because higher temperatures will break down some toxins that might be created by some bacteria during a longer period in the "danger zone." Spending more than a couple hours in the "danger zone" can create toxins in poultry that could still be present if the final temperature is still only 140F/60C or whatever. This is something not mentioned in most sous vide guides, which tend to be focused only on Salmonella death curves, but it's a legitimate concern if you're cooking a very large hunk of meat in a water bath at low sous vide temps.