Yeah, just buying Estates with those decks would not work.
I was thinking how I would play this. My deck produces $3+P. I guess I would start by buying Alchemists. Jaybeez could do the same, buying one every turn with my deck, without making his deck useful for me. I would get 6 Alchemist and he would get 4. Because he didn't keep his Potion, his deck could potentially fail to draw itself sooner that mine. I could then buy a Silver, which means I could start buying Cities. If he did the same (with my deck), we would split the Cities. But at some point someone could start buying Duchies instead. If he started buying Duchies too soon, his deck would soon stall. Also, if the Duchies run out first, Cities start producing $, meaning my Possessions could buy something with his deck if he has some Cities. Let's say he buys a couple of Cities - by that time I would have three - before switching to Duchies. We both buy a Duchy a turn, splitting them 4 each. Now his deck produces $2 and mine produces $8 (two buys). We could switch to Provinces and Estates. I could buy a Province and two Estates each turn, he could only buy a Province and one Estate. Maybe if he had kept his Potion, he could keep from stalling. Potentially with all that green any of us could stall at some point though, especially if we didn't draw our Potion. I don't know if going for Estates with the Provinces would be that smart. Maybe for him, since that's his only shot.