The Content Aware fill in Photoshop is designed for removing things from photographs, not from gradients in logos. It takes parts of the surrounding image and tries to fill in the selection with similar textures. It's called "Photoshop" for a reason!
I think you are making this more complex than it needs to be.
What I would do is fill over the existing text and background with a new background, and then add new text.
- Make a selection around the entire area that encompasses the background and text
- Use the Pen Tool if you want accuracy
- Turn the path into a selection
- create a new layer
- Fill it with a gradient - sampling the existing gradient if necessary to recreate it
- Add new text
Also I might add that using Photoshop for logo design/editing logos is less than ideal. Logos are best designed using vector image editing software, such as Adobe Illustrator, CorelDraw, or the free software Inkscape. Recreating a logo in vectors would be the ideal scenario. The main benefit is that vectors are rescalable without degradation in quality, also editing them is easier.
Using Photoshop for logos is a bit like hammering in a screw in, rather than using a screwdriver. Sure, it'll get the job done if you hit it hard enough, but it's better to use the right tool for the job if you want the best results.