Here are the numbers you gave above:
27055.6 Correcrted Watt hrs per week of AC load
1127.317 Amp Hrs per week
10.42 Amp hrs per week DC load
1,137.73 Amp Hrs per week of AC/DC totals
162.53 Daily Amp Hrs Used
702.14 Amp Hr capacity per Batteries.
Do you have a link to where you found this? Or you could upload the spreadsheet you filled in by clicking on your username and going to your Files section. Then we can all look at it. One thing that's missing is your largest power use at any one time. That's a factor in selecting an inverter.
It looks like you gave it both AC and DC loads.
It looks like your total weekly usage is 27055.6 watts of AC loads and a system voltage of 24 volts. 27055.6 watts / 24V = 1127.316 Amp Hrs per week for the AC loads.
It looks like you gave it 10.42 Amp Hrs of DC loads, which when added to the above 1127.316 Amp Hrs gives 1137.73 Amp Hrs per week of combined AC and DC loads. 1137.73 Amp Hrs per week / 7 days per week gives 162.53 Amp Hrs per day.
I'm not sure what how the 702.14 Amp Hr capacity per batteries was calculated but I'm guessing it was something like the following...
You told it that you wanted 2 days of battery storage.
162.53 Amp Hrs x 2 = 325.06 Amp Hrs.
You don't want to discharge your battery bank past 50% of its capacity. Doing so shortens the life of the batteries. The less you discharge them the better. But this means you need twice the capacity (for a maximum 50% discharge.)
325.06 Amps Hrs x 2 = 650.12 Amp Hrs
Then they probably added an extra 10% or so for inefficiencies to get 702.14 Amp Hrs.
I would have just added 25% off the top to your needs instead of counting individual inefficiencies - a pretty standard industry practice - but that's fine.
Volvo Farmer had recommended Eight T105s (8 T105 Trojan Plus batteries, I'm guessing it's the Plus version). They are 6V each and 225 Amp Hrs capacity. For a 24V system voltage you'd need 4 in series to get to 24V, but that would be only 24V and 225 Amp Hrs. Series means connecting positive to negative and that voltage adds but Amp Hrs stays the same. So to increase the Amp Hrs to what you need, you'd need to connect 3 of these series strings in parallel (positives to positives, negatives to negatives.) When connecting in parallel the voltage stays the same but the Amp Hrs add. So 3 x 225 Amp Hrs = 675 Amp Hrs. So for 2 days of storage your battery bank would consist of 12 batteries (4 x 3) giving a total size of 24V, 675 Amp Hrs. That's a little less than 702 Amp Hrs but this is all pretty abritrary since you have a 12kW generator always at hand.
You can shop online for the price of T105 Trojan Plus batteries to get an idea of cost. Alternatively you could go for fewer larger batteries.
So you'll arrive at your cottage and turn on your generator first thing. You'll then turn on the pump to get some water. The inverter will see the generator power and pass through power to whatever loads need it. At the same time the inverter will start charging the batteries. They will be partly discharged from the previous weekend and have lost some charge during the week (about 2% per day at room temperature, more if colder.) Remember, we sized the batteries according to your needs to use up 50% during 2 days. The inverter will Bulk charge for a while, then go into Absorb charging for an hour or two. This gets your batteries up to about 80% state of charge (80% x 675 = 540 Amp Hrs.) As batteries get more and more charged, the less current can be pushed into them. So the inverter will go into Float charge mode where it is using a tiny fraction of the generator's output to charge up that last 20%. Depending on how discharged the batteries were this whole process could take as long as 6 hours. With the Outback you tell it how long to stay in Absorb mode and how long to stay in Float mode. I don't remember for Magnum.
Another consideration is that a discharged battery in below freezing temperatures will crack as the water turns to ice. A fully charge battery will not freeze. So what will you do during the winter? Without a solar system to keep the batteries topped up all winter, you'll have to take the batteries home. An alternative is to install an Automatic Generator Starter (there's one built into the Outback, but there are others, Magnum has one and there are standalone ones) where the AGS will start the generator as needed to keep the batteries charged. I wouldn't trust it to work all winter though.
-Steve
http://rimstar.org/renewnrg
PS. Sitting here getting over a cold. Oddly enough, writing all this works well so I kept going. :-)