There are many schemes for storing energy besides batteries. Unfortunately, not many of them are well suited to storing large amounts of energy for long periods of time in a garden apartment.
I have about the largest capacitor bank of anyone I am aware of, although there are probably people on here with larger banks, but I am not aware of it. My capacitor bank is 110 Farads at 64.8 Volts, and if you were to buy it retail it would cost a few thousand dollars retail. Even if you could utilize every Joule of energy that that bank can store, you would only have about 64 Watthours of energy, equivelant to using about 5.3 amp hours on a 12V battery, and much less than what you already have. The reality is that for me, I can only use about two thirds of that storage which falls in a useable voltage range for me. In short, storing the energy in capacitors for you is likely impractical.
You are using your batteries to store power, batteries are less than ideal, and this is a bit problematic for you. If batteries were perfect, and did not self discharge, you could just get a larger battery bank. Unfortunately, all batteries self discharge to some extent. The larger you make your bank, the more energy you will lose to this self discharge. You will have to figure out the optimum battery bank size which may be a bit larger than what you have, I am not sure, but batteries are likely the best option for your described situation. Rich