The latter. Is that the wrong way to go about it?
Yes. All you are getting is a picture of the widget which is being painted into the cell as an image. It's not a widget, you can't interact with it.

There are two things you can do:

1 - Create actual list widgets and set them as the index widgets for the cells you want. QTableView::setIndexWidget() If the table is of any significant size, you will take a huge preformance hit. The widgets are disconnected from the model, so you have to manually update the widgets when the model changes, and if the model needs to change based on selections from the list, you'll need to do that yourself as well.

2 - Create an item delegate based on a list widget and install that on the cells where needed. Item delegates are intended to be used when editing a cell's content, and are normally not visible when the cell does not have focus.

Neither choice is optimal for what you are trying to do.