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Yes, you are right, you cannot add additional text to the taxonomy pages, so it makes sense to solve it with a gallery.

Is it possible to change how those read? For example, I would rather they say
Client = For More Information
Works = Product

Yes, you can change this. Just open the file “sevenleague” in the folder “languages” and change the text.

The slider in the portfolio will show all attached images to the portfolio entry, to add new images in the slider just edit the portfolio entry, click the “add media” button above the editor, upload the images and after uploading, just close the pop up window and save the post. WordPress will attach the images to this project and display them in the slider.

If you want to hide the “Created: “+date, please go to WP admin -> Appearance -> Theme Options -> General -> Extra CSS Content and add this:

.portfolio-single-details .work-details-p {
display:none;
}