Been messing around solo wise for awhile trying to get something that works with Counting House.
Obviously this isn't entirely applicable, as solo and two player games are very different, especially when we're talking about using Mountebank to slow down the game.
The benchmark has been 28 turns or less in a Colony game, as pure Big Money takes about 30 turns to get all Colonies.
Warehouse/Counting House/Cache is just too slow. Its too hard to acquire a decent number of Counting Houses and draw them at the right time. You then either get overkill $ or not enough for colony, and all in all it takes about 30 turns.
Golem / single Counting House relies a lot on drawing the golems early in the shuffle, and in getting $4P relatively early and frequently. Certainly it doesn't seem like you want more than $11 of copper, and once a Golem is bought buying any other treasure other than Platinums lows the Golems coming up too much to be worthwhile. Again, about 30 turns in solo.
I'd agree its marginally stronger than pure BM, as it can spend misfired turns picking up lower value green cards with less slowdown. Its also very high variance, as you can luck into consecutive golem turns, or draw the potion with $3 several times.
What seemed to work well, however, was Golems + single Counting House + Chancellor + a single other enabling card (either Warehouse or Worker's Village), getting coppers on weak turns, one Cache when there's time, and getting gold and platinum when possible. I've no idea why, but this one seems to gel nicely, with Golems being bought frequently, the occasional turn of $11 just coming out of money, and golem often setting up an $11 hand even if it doesn't draw Counting House/Chancellor. Also, the deck can acquire provinces with no significant slow down to the engine. All in all, this seems to give me 24-26 turns fairly consistently.
Thats not to say we're looking at a strong engine here, but rather a viable good choice in a particular extreme kingdom layout. How this solo strategy translates to multiplayer, I dont know.