Earlier quoted context omitted.
I was able to accomplish this by doing each test within its own transaction session that gets rolled-back after each test. This way I'm allowed to modify the database to suit my needs for each test, then it gets magically reset back to its known state for the next test. Transaction rollbacks are very quick.
Unfortunately a lot of our tests use transactions themselves because we lock the user row when we do anything to ensure consistency, and I'm pretty sure nested transactions are still not a thing.
You can emulate nested transactions using save points. A client uses that in production. And others in unit tests.