I think I'm less concerned with how well it does with dual-types -- although that is a concern -- as how mandatory it would be as an opener. This is crazy strong, usually better than every other trash-for-benefit card in the early game. It's better than Apprentice at trashing Estates, for example, and way better than Apprentice, Salvager, and Trader at trashing Coppers. It's on a par with Moneylender at trashing Coppers, but Moneylender is completely dead if you don't have a Copper to trash, so this is wildly stronger than Moneylender, even above what you can account for with the price increase. In the mid-game, when you have a higher density of cards you want to keep, I think it's probably more balanced. But I fear it would be basically mandatory to pick up within the first four turns.
You might be able to at least partially fix this by including a Potion cost, so that it cannot be obtained too early. I'm not sure if that's enough of a nerf, though. You might also have to reduce some of the specific bonuses, too. Perhaps removing the +1 Action for Victory cards is an interesting idea.
Ultimately, with the right nerfs, you probably won't have to do anything special for dual-type cards anymore. After all, there are no dual-type restrictions on any other card that cares about type: Tribute, Transmute, IronWorks, et al, just work with dual-type cards as appropriately strong combos.
