Are you working with paths ?
Make selections, convert to path, then stroke ?
This kind of logo design is a job for Inkscape. Its doable in Gimp but harder to do.
Especially for the fine tuning steps you are currently dealing with.
I think you are having difficulties with the design because you didnt set up a proper "grid" of guides and elliptical selections that you can convert into a path and stroke.
Gimp offers a lot of help with options like 'Expand from center' and 'Fixed Aspect Ratio' for the Elliptical Selection Tool.
Make sure they all have the same center.
When you got the selection right, convert it into a path in the Selection Menu, then go into the Paths Tab and Stroke it from there.
Work with many layers and subtract bits you dont need with more selections and delete.
You can colourise the stroked paths, with the lock alpha channel option in the layers tab (background must be transparent), and then drag and drop the colour you want.