Your method may be ok for inductive loads, but it way overestimates the power required for resistive loads (are you really going to use 120 * 15 * .6 = 1080 watts of lighting?).

And you don't have to run everything at once. Run the fridge till the compressor stops, then don't open the door. Buy a window AC unit ($110 gets you one with a remote control!), and just cool one room, etc. You don't need a 7000 W generator. Sure, it's nice to have and will be most convenient, but you can get by with less if you'll only run a few things at a time.