I played this solitaire for nearly an hour and really couldn't get it to work. When I opened potion/NV, I often drew $2 in the second shuffle (at which point I can either get a second dead card, pass for a turn, or start treating the NVs as blind draws, all of which are pretty unappealing options) and occasionally drew $1P (which is a disaster for obvious reasons). Potion/silver was much better but even then I was pretty unsure what to do with another $3 draw. Another silver? OK, but that really gets in the way of the apothecaries.
I found that this combo works much better if you have a cantrip that also gives coins. Peddler worked ok, though there's no buy naturally in this combo. Wishing Well was great for obvious reasons. Bazaar was ok and so was Market. In general, with a cantrip +$ and opening Potion/Silver, I was generally able to hit 4 provinces plus 2-3 duchies around turn 16. I had some fast games where I hit 4 provinces plus a duchy around turn 14, but I also had some games with no obvious support where I was still floundering around with two provinces at turn 18.
My feeling is that this combination tends to be a bit swingy. If you hook up your apothecary with a native village early (which is harder than it sounds, because sometimes you draw 4 cards and sometimes you draw 2-3 but the remaining ones are silver and apothecary), you're in good shape and can usually be at least competitive with Big Money. And when that happens I definitely feel like my deck has decent staying power, even to duchy dance, because with 3+ apothecaries I'm typically able to connect my NV to some green every time it come up. But if you don't hook up the combo early or get a couple of bad draws, it's way too slow, even on a board with no accelerants.
MMM, do you have a sample game illustrating how to play this combo? I searched council room but couldn't really find a good example.