I agree with the OP's opinion that selecting the gold trim is an interesting solution. We want to take the blue components in the original image and turn them red without changing the blue components in the trim.
Here is an approach that uses GIMP's layer masks and color channel extraction to separate the gold trim from the rest of the image so we can process the non-trim parts independently. Maybe it's more than you need, but my curiosity got the better of me. Since I went through the process already, might as well share!

I noticed the green channel in the original image could serve as a decent mask for the trim so let's start by extracting it:
- Create a copy of the original image on a new layer. Name this layer "TRIM MASK".
- Use Colors/Components/Extract Component on this new layer to extract the "RGB Red" channel.
- Select this entire layer and copy it to the clipboard
- Hide this layer, we are only using it to create a mask.
Now we have a decent mask to separate our image. Let's create a layer of gold trim.
- Create a copy of the original image on a new layer. Call this layer "GOLD TRIM".
- Right click on this layer and select "Add layer mask". Initialize to black (we will change the layer masks in the next step).
- Select the layer mask (the black rectangle next to the layer's preview), paste the red channel we copied earlier, and anchor it
- Hide the original image
Now, we have a layer that is relatively opaque where the gold trim is, and transparent elsewhere.

You can then add a layer of a flat color underneath. Call this layer "BACKGROUND".

The flat color looks a bit artificial, so let's bring some of the original texture back in by extracting it from the original:
- Create a copy of the original image on a new layer between the flat color and the gold trim layers. Call this "TEXTURE 1"
- Use Colors/Components/Extract Component on this new layer to extract the "RGB Blue" channel.
- Set the channel blending to Grain Extract
- Play with the layer Opacity until you get a satisfying result.

Finally, for fun, I stumbled on this result that I really like by adding the following layer:
- Duplicate the "GOLD TRIM" layer and place the duplicate just underneath it. Name this duplicate "TEXTURE 2"
- Use Colors/Components/Extract Component on this new layer to extract the "RGB Blue" channel.
- Select the layer mask and invert it using Colors/Invert
- Set the layer's blending mode to Multiply.

I hope this helps!