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I have just been taking a look around some electronic component distributors and I've seen some flat (2.3mm at it's thickest point) GPS antennas. They're quite expensive though, but worth it for sure, so I suppose that if I manage to find decent AA lithium batteries I could probably hide the whole thing inside the handlebar.
A hole in the handlebar would allow me to route the antenna cables out and I could just wrap tape around the antennas, putting the antennas in a place where I know I'll never pressure.
I guess I could modify one of the caps to install a enable button of some sorts.
I'll order some stuff to prototype it tomorrow.