Hofstadter's stuff is not remotely GOFAI. Have you read his books or looked at any of the projects?
Hofstader begins with symbolics but definitively goes off them.
The point of something like a "strange loop" is that it can't be encompassed by an ordinary symbolic system.
For someone who takes the idea of a system that's impossible to model further, IMO, check out the biologist Robert Rosen's Life Itself and Essays on Life Itself. He pushes more in the direction of complex systems theory than self-reference (maybe a physics version of the same idea?) but his writings are brilliant. Less fun than Hofstadter's, but more rigorous and with a necessary appreciation of the biological and physical sciences. Anyways, I'm rambling.