Wouldn't it be possible for a process to ask to be pinned to a specific CPU core, or the OS to handle programs with extra tags indicating their ISA requirements, so that it could restrict the scheduling to those cores matching the requirements?
You all would probably find the "QuickIA Software Support" section interesting, they go through a few issues you run into when you have incompatible micro architectures running in a single system. It also might help illuminate where Intel's head was at during the early research phase of creating a heterogeneous processor.
I decided to search for SMP, which stands for Symetric Multi Processing, to verify its definition. This acronym is used for hardware sporting several identical CPUs, which is what we've seen so far in the x86 world.
The opposite is called AMP, for Asymetric Multi Processing. The Wikipedia article on the subject describes several OS level strategies to handle that sort of hardware.
If the processor faults for an invalid instruction, it can simply trigger a migration to another core. The OS should be able to do it.
Even if it's randomly assigned to a different core, eventually the process will end up on a good one.