Your power consumption are not uniform distributed during the whole month - you just have peaks from time tot time (door+lights). So you have to design your energy storage (battery) for that peak consumption.
Your door has a nominal current rating of about 125A (for a 12V battery) and your lights are about the same. So, if you want to run them at the same time you need to extract 250A from your battery.
The manufacturers recommend a C/10 - C/5 discharge rate for the battery, thus you might need a minimum 1250A battery. Still you could extract more than C/5 but the available power will decrease.
10kWh of monthly energy, for a 12V/250A load means almost 4 hours of running on battery (durring the entire month). If you use the door/lights once a week, that means an hour at (almost) full power every time. To limit the battery discharge at 50%, you should have a battery rated at 12V/500A (theoretically).
To charge such a "monster" after a deep discharge (50%) you need a least a C/10 current, that means 50A.
From a 40W PV panel you could get a maximum of 2.5A (16V) and that's almost a trickle-charge for such a battery.
You have two solutions: to buy a larger capacity PV panels (not economically) or to have a much larger battery bank to not discharge them very deep, so you could keep them charged with a small current (2.5 - 5A).
There is a more economical solution for this situation: to buy a 2-3 kW gas generator and to use it just when you need it.