I've found conquest BM to be pretty strong. It won't beat a decent engine I don't think, but on a semi weak board I think it should be the standard play. You want to open silver silver (or equvilant) and just buy conquest every turn you can. If you spike 6 on turn three or four I think this becomes VERY strong. But even with normal shuffles you should be able to conquest almost every turn by turn 5 or 6. That's two silvers and two points every turn. By the time you opponent wants to green your deck has so many silvers it can reliably hit 8 and you have a bunch of points. Anyone else ever do this? I think conquest BM is a thing and should be the stand play on many boards. (Or maybe I've gotten lucky the 4-5 times I've done it?)
Interesting question. It's clearly stronger than Harem, and while an extra Silver does not seem like that much, that's essentially the difference between Harem and a 2 VP cantrip (i.e. double Great Hall), which should probably cost less than $5, while Conquest costs the same as Harem. And with another Silver gainer on the board, Conquest-BM may well become dominant.
OTOH, Harem-BM is hardly better than pure BM, I think. This calls for simulations!