The thing is that some cards refer directly to Copper, though, and because there's a when-trash benefit, I want it to be able to be trashed by Moneylender.
And then when someone plays Mountebank, can I choose to gain one of these (and then fail to do so because they aren't in the supply)? Although I see what you're going for, I simply don't think you can create a new card with the same name as an existing one... just too many potential issues.
It's the same issue as when one of your Shelters gets Swindled and Poor House is in the supply; your opponent has to give you a Poor House because he has to choose a card in the supply with Cost 1 to give you. Likewise with Mountebank, you have to gain a copper from the supply, so you look at the supply for any cards with the name or type "Copper", and your only option is the basic Treasure costing $0. If a card existed in the supply with the Name or Type "Copper" that wasn't the one we know and love, you could choose to gain that instead. However these Trinkets are not in the supply.
The solution I'm going to go personally go with for these interactions (in lieu of any other ideas) is to give all trinkets the type "Copper". So, for example, Trinket Box will be Treasure-Victory-Copper, and give you "1VP for every 2 Cards with the Copper type".