Now that I understand that you're looking for 1 bbl of each style......
I would advise against doing six 5 gallon batches or even three 10 gallon batches for the sake of consistency and sanity.
But if you really want to do it on your system, you will have to brew at least 3 times to yield 31 gallons.
And I would forget about Corny kegs for 2 bbls of beer. You are in no way capable of handling the logistics of carbonating and cooling 12 corny kegs of beer with what you have currently.
Let's say you say F it and you're going to do it anyway. Brew three 10 gallon batches and get yourself one of these:
or if you have money to throw around get a nice stainless conical.
You need to clear your schedule for a couple of days and brew consecutive batches. Or maybe play with the idea of using the first 10 gallon batch to build up your yeast.
After your near bbl is done fermenting, you need to keg in sankey kegs. That's a whole different post though.