A 7A load at 28.8V (full charge, depending on battery type) is 201.6W. Assuming that's the continuous average load (since that's the number we need), that is 4838Wh/day. Your batteries store about 6000Wh, but only about half of that is usable without shortening the battery life. Even less capacity is usable in the winter when the batteries are cold. That means your batteries store about a day's worth of energy. You'll need larger batteries or huge panels to compensate for the lack of storage. Omaha, NE has a minimum of just over 9 hours of daylight in the winter, so you need to accumulate 4838Wh in 9 hours, which is 537W. But your panel ratings need to be about double that to account for the low irradiance and off-angle lighting early and late in the day, so you would be looking at about a 1kW array. However, and I know from experience (I'm a Husker) that it's often overcast for days in a row in Omaha in the winter. Since your batteries must be fully charged every day to avoid the possibility of power failure, you'll need huge excess panel capacity to deal with extended cloud cover. You'll also need to keep the panels at a steep angle to shed snow. All things considered it's not unrealistic to size your panels at about 8-10X the initial calculation. That's roughly a 4-6kW array to handle your load year-round with those batteries. It would be much cheaper to invest in more batteries so you can use a smaller array (perhaps 1-2kW) and ride through periods of cloud and snow cover with your storage capacity. Remember that only 1/3 to 1/2 of the rated battery capacity can really be used, especially in cold weather.
For a different approach, a solar power calculator online predicted that a 1kW array in Omaha would produce 91kWh during the month of December (the lowest month), which is an average of 2.9kWh/day. So the array can be expected to produce about three times its rated power in kWh daily. Since you need 4838Wh daily, that requires about a 1.6kW array. However, this calculation does not account for the duration of bad weather - only averages over month-long time spans. This means that to use an array of 1.6kW (or perhaps 2-2.5kW to be safe) you would need a battery bank that stores enough power to get through any cloudy periods. That's probably about ten times the storage you currently have.