Plumbing – Which of these is the sewer cleanout

The best option that I can think of would be to have the sewer lined. This company is simply the first Google search result I found:

http://www.dontdig.com/drainlining.php

The premise here is that a flexible liner is inserted into the pipe (usually using air - think of it as turning a sock inside out) and then the liner is hardened in place (water activated? resin?). The new liner will bridge any cracks or breaks in the pipe as well as any gaps in the joints.

I would also suggest actually getting the section of drain in question inspected...you will really want to know what the true problem is before deciding on the proper corrective action.

Here's my speculation, based on your description and my experience. It is just a theory. Do not commit any resources based on this without collecting corroborating physical evidence supporting it. A direction to investigate at least.

The main floor plumbing goes out to a septic tank. The pipes were not placed lower because there was no need, it just meant digging deeper outside. No one wants to do that without good reason.

When the city sewer was installed, the basement construction tied into it, but the old plumbing was never redirected, it remained on the septic tank. Not the best scheme and possibly illegal, but I'm not surprised someone did this.

It is highly probable there is nothing below to the basement to tie into. The sewer may not be much lower than the basement drainage exit. Anything placed lower than this will likely need to drain into an ejector pumping chamber.