Question: Could it be possible to have a system installation where you can dual-boot using either the ?Linux kernel, or the GNU Hurd, so that everything but the kernel is shared?

Answer: Given that both Linux and GNU Hurd are using the ?ELF binary format, this could indeed be made possible, if all programs agreed to rely on only one abstraction layer, for example the standard C library (glibc). (Additionally, for example for system calls that are not covered by glibc calls, you'd need to be able to reliably trap and emulate these.) However, Linux' and the GNU Hurd's ?ABI's have sufficiently diverged, so that this is not easy to do. That's why you can't currently install a system in this way, but you need a separate installation of the userspace suited for the Linux kernel, or the GNU Hurd.