What are the advantages of installing an aerobic septic system?

the more time you spend on it, the best you will manage.

should go through the roof just like the black water

It seems like septic tank need to be pump out. Call a local contractor or professional for inspection and pumping.

sounds more like the drain line is clogged between the shower and the main stack, and shares venting and drain with your kitchen sink. Have a plumber run a drain snake down from your kitchen drain (after the 'P' trap ) to clear the line. A covered over floor drain should have no effect on the back-up.

A sewage treatment system utilizes two types of bacteria to break down waste products, aerobic and anaerobic. Aerobic bacteria need oxygen to live and do their job of breaking down wastes. Anaerobic bacteria need an absence of oxygen to do their work. The first tank of a septic system contains the anaerobic bacteria the second tank and drain field ( or drywell) contain the aerobic type of bacteria. Anaerobic is needed to break down solids but it cannot do the job alone so when the waste leaves the first tank air is introduced to kill the anaerobic bacteria and the aerobic bacteria is used to finish breaking down the waste.
Hope this helps.
Bob

Contact Uni-line for replacement clock motor
http://waterheatertimer.org/Paragon-timers-and-manuals.html#42000

Advantage 8025 mechanical timer that gives short time intervals from 1 minute to 27 minutes.

If you are using for septic tank pump, then you have 1 circuit, so you do not need the 8025 to control 3 circuits.

You can install digital timer (EH40 240Volt, or EH10 120Volt) and also get 1 minute intervals.
http://waterheatertimer.org/How-to-wire-EH40-hot-water-heater-timer.html

If you need further help, I’m available over the phone at https://www.6ya.com/expert/gene_9f0ef4df2f9897e7

A septic tank is a key module of the septic system, a small-scale sewage handling system common in areas with no joining to main sewage pipes provided by local supervisions or private houses. Like TGWasteWater.com