I decided to apply a hack to 4.19 and see if I could get the eGPU to
initialize.  I noticed that this code in /drivers/gpu/drm/amd/amdgpu/atom.c

if ((jiffies_to_msecs(cjiffies) > 5000)) {
        DRM_ERROR("atombios stuck in loop for more than 5secs aborting\n");
        ctx->abort = true;
}

is where the error is being thrown, so I thought I would try giving the eGPU
more time.  I increased the 5000 value to 15000, recompiled the kernel, and
tried to attach the eGPU.  Unfortunately I received the same error, but this
time after 15 seconds of trying to initialize the GPU.  Should I increase the
time even more?

I'm not sure if the issue is actually related to not having enough time, or if
it's something else entirely.

I'll bump it up to 30 seconds in a final last ditch attempt.