I would like to suggest that you don't use GIMP for this. I know you asked for GIMP, but this would be much easier done using the free vector image editor Inkscape, by making use of its Envelope Distort path effect.
Here's an example of what can be achieved. I have tried to show the control paths which show how the distortion works.
Here's how to do it:
- Create some text, and click Path > Object to Path. This converts the letters into outlines so that they can be distorted. After this has been done, like in GIMP, the text is no longer editable as text.
- Click Path > Path Effect Editor. In the dialog that opens, click on the dropdown under "Apply new effect", and choose the "Envelope Deformation" option. Then click Add.
- Select the top blend path "Edit on Canvas" button, and using the "Edit by Nodes" tool, click on the path to bend it or move the nodes. You can click and drag the pathto bend it, and you can adjust the bend of the paths with the Bezier handles.
- Do the same for the left, right and bottom paths - and try to position them similar to the above example
Once you have completed this, you can then export the image as a PNG from Inkscape, and use it in GIMP.