Turdpress is crap for EVERYTHING, except maybe grandma's blog.
It's hard to use, full of bugs, has serious security issues, is not intended for e-commerce and so on.
Furthermore, it is impossible to maintain it. As soon as you fix a problem, the update introduces another problem. E-commerce sites have only one function to sell products. Anything that takes away resources from this function is something that needs to be dropped. But the most common problem, spending time to keep everything running, can not be thrown away, unless Turdpress is written and something else used for e-commerce.
The solution for e-commerce? Use something that is intended for e-commerce ONLY. Even most of them are bloated railroad wrecks, but at least they work better and faster than Turdpress. And since they are designed for e-commerce, they are MUCH easier to use when managing an e-commerce site.
Ideally, you should code your own site instead of trying to use an "all-around" solution. Ecommerce websites are one of the easiest to code sites as e-commerce sites require only a few features.