Thing with the spices is that medieval spices were much more varied than the few commonly available today - many are now out of fashion (cubebs, long pepper, though that is gaining traction, grains of paradise etc.).
I suspect the reason many have dropped out of use is down to suppliers not really wanting to bother and the similarities in flavour profile mean the the common ones are good/close enough.
The medieval cook would, however, be fascinated by the containers - screw top and air tight. If you could work out a way of making those...