Would an Apothecary/Counting House/Cache strategy work well?
... So what exactly is your plan here? Stack Apothecaries to draw basically everything except the Counting House, then play CH on the next turn? But the CH might be drawn by the +1 Card on the Apothecary, and even then, instead of playing CH on the "off" turn, you could just, you know, reshuffle, get an Apothecary in that hand, and start stacking Apothecaries again. As much as you'd expect these cards to synergize, I think they actually conflict.
Cache is amazing when you actually want Copper, though, yeah.