If I understand it correctly you are dealing with your own system and all other systems are wordpress instances with woocommerce extension, right?
Have you checked what the root cause of the issues was? Were those scenario’s covered in the tests? Did you update the tests to better cover those scenario’s? It might not always be doable, some scenario’s can be tested much easier via the UI, provided that you have the infrastructure to test this.
I read that you have unit tests and that you have mocked some of the request libraries. What you could do is not mock those libraries, but use only production code of your platform and mock/stub wordpress and then either extend the integration tests, or create UI tests with Selenium. (probably depends on the issues that you ran into) However, this might not give the confidence in the tests that you need?
If you want to use a real wordpress instances to test, you could either generate an instance from scratch and dispose it after testing, or you could have one wordpress environment that you restore to the default state before each test. Either way, you probably need to use some database scripts to provide content/product data/users on the wordpress system that your tests depend on.