A -0.3 volts will not hurt any capacitor, even one rated for 5 VDC. Also Schottky diodes are available in very high current modules if needed.
A negative 3 volts may hurt them by confusing the chemicals in the dielectric, much the same as reverse charging a battery. But there the similarity ends. Capacitors can be drained to zero volts for a long time, yet are ready to use again if needed.
Supercaps have a higher leakage current when power is first applied but with time the leakage current drops way down.
There is no 'perfect' circuit to do want you want without a MPU to monitor and use MOSFET's to act as a bypass diode with near zero voltage drop.
If you can keep the reverse voltage under -1.0 volts the capacitors should be fine.
EDIT: Also something to consider is load balancing by placing a 1 Meg ohm resistors across each capacitor. This ensures that they charge up equally and maintain an equal voltage across each one. The penalty is a leakage current of 1 uA per volt of charge on each capacitor.
Addendum: Please see the following link for details of many types of super-capacitor. The small PCB mount type generally have a gold foil or carbon conductors, so do not worry about them going bad due to lack of use. Their only real enemy is over voltage or a high reverse voltage.
A statement from that article says:
As of 2015, a CDC supercapacitor offered a specific energy of 10.1 Wh/kg, 3,500 F capacitance and over one million charge-discharge cycles.
I do not think your supercaps are in danger from just sitting around, but watch out for lead corrosion due to moisture. Also, the PCB mounted type can charge quickly but may supply only 10 mA to a short circuit. It is due to how electrons are 'trapped' inside it and 'migrate' a long winding path to the pins. A cheap 1N5822 schottky diode is plenty good enough, unless you want one with a lower Vdrop.
For better charge-balancing you can use 10 K or even 1 K resistors. Add a 4PDT relay power by 3.3 or 5 VDC to engage the 1 K resistors when charging. When not charging the relay changes contacts to the 1 Meg ohm resistors for maximum storage time.