OK, my dear audio friend Doede gave in DIYaudio.com the advise, to try to use an ultracap in parallel of the output of the batteries.
So I ordered his suggestion: The Eaton https://www.digikey.de/de/products/detail/eaton-electronics-division/XTM-18R0626-R/10461229 a 18V bank.
I understand that there is an initial loading-procedure, so I could for example load the super-cap to the 16.3V with an external CC/CV-PSU (mine can do up to 10A) before connecting it to your battery supply (in order not to overload it).
Now, let think through what will happen when I connect it to your Battery-Supply.
I guess there are two options how to do it:
A. Connect the supercaps to J5: Than we have them as well in paralelel when your normal 13.5V standby-Reg kicks in…not sure if that is smart…if this will destroy the reg (?) either because the superreg has to high voltage at the output of the reg od drawing too muich current to charge itself again if the supercap has less than 13.5V…?
B. Connect the super cap to J4: Depending on how the relays work (need your input here…): If J4 is only active when batteries are “on”, than the supercap would try to charge itself from the batteries which still have the clocks supppled with current as the super cap hopefully did not get discharged by the clocks from last usage (to be verified…)
I am thankful for your thoughts …