I haven't had a good look at the log because it isn't pretty enough, but surely something that plays 1-2 Thiefs/turn and embargoes Gold crushes BMU. You can even play double Tactician for a while with a bunch of Minstrels just to play 3 Thiefs/turn until your opponent is out of money.
The fact that BMU beats what you ended up doing is irrelevant except in the specific case of your opponent actually playing BMU and your strategy being your response to it.
The second half of this, so much. The first half, I am much less sure. Well, that probably beats BM/No actions, but I am unsure that it's actually the best strategy on the board. It's very slow, and a good money player with appropriate draw cards, countermeasures, and more importantly, embargoes of their own, should be able to hold off an engine player, I think.
