PCI cards are enumerated and assigned addresses in the host's address spaces (both memory space and IO space). The cards can DMA to anywhere in main memory and in principle even DMA to each other bypassing main memory (though this is rarely done outside of specialist kit from the likes of National Instruments).
Drivers for PCI cards don't expect to pass requests through lower level drivers. They expect to be able to talk directly to the card through the memory and/or IO map.
You can try and fake memory accesses, for example by using the virtualisation features of the host CPU but you are likely to run into significant latency issues.
I therefore find it unlikely that such an adaptor can be made to work acceptable with the existing drivers for the cards. The only viable way to make such an adaptor would likely to be to re-engineer the drivers for each card you want to work with it, carefully deciding what tasks to keep on the host computer and what tasks to move into the adapter.
If you want to use your hardware with the standard drivers then you will need an appropriate PCI-like interface to the host, such as cardbus, expresscard or thunderbolt.