turn on both elec. & propane water heating. It''ll help some on water heating and recovery.
Check your propane only heat temp, elec. only heat temp. A cooking thermometer in a glass of heated water may show the thermostats are set too low.
120 F is optimal, legal commercial. You may set your temp higher on your ' cold' water heater to give you longer showers.
Elec. water heating is notoriously slow and 'cool ' used alone. By law, they are set at a max.of 120f. 6 gal. just cant do what you want at that temp. and slow 10 Amp 10360 btu recovery rate.
An option for you is
Burn Propane, its 30,000 btu heat rate. set your propane regulator thermostat higher. you will get the hot water for what you wish. Educate all your family that it is very hot, to be careful of scalding.