Ok, I've now done quite a fair bit of testing of this card. Some conclusions:
(1) It's EXTREMELY overpowered at $6. On a weak board for it, it feels about right for a $6 purchase, but on even a just-okay board for it, it's a must-buy. $7 feels better, and then there are still a great many boards where it dominates (but, I think, not brokenly so).
(2) A problem with the "borrow a card" version: on complicated turns (which MoD contributes to, since it can be whatever missing link in your action chain you need it to be), it got to be very confusing to remember which cards go back to the supply and which get cleaned up. It would be easy to make a mistake and shuffle in a borrowed card. We worked around that problem by playing borrowed cards upside-down on top of MoD (we were using blanks for it), which helped, but it still slowed down the game and felt like too much mechanical manipulation.
(3) The "invisible copy" version has its own problems: it was hard, in a complicated action chain with multiple MoDs, to remember which MoD was what, which made keeping track of actions, coins, and buys tricky. I think this was a lesser problem overall EXCEPT when duration cards were involved, where remembering, on the next turn, which MoD was what was just far too tedious and confusing. And then, remembering at the end of the turn, which MoDs stayed out and which ones got cleaned up -- just too complicated.
(4) Thus, I think the easiest version to play is probably the invisible copy version that doesn't work on next-turn durations. I'm not sure losing the next-turn durations is worth it, though, and in any case that feels more compatible with the borrowed copy version than the invisible copy version.
(5) Of course with a computer program these issues are moot.
In terms of strategy/gameplay, it's extremely interesting. I speculated on this in an earlier post, but the main thing I missed was how usually it plays when it comes up before your engine is fully running. For example, if you draw it with a strong terminal, the correct play is usually to copy the best non-terminal in the kingdom -- even if that's Pearl Diver. Because your other options are to not play it at all, or to use it to mimic the terminal you've already got, which amounts to the same thing. (Or you can mimic a better terminal, but I'm talking about the situation where that terminal in your hand is the one you really want.) On such a turn, of course, MoD is a very weak card, but this is a specific situation in a specific type of kingdom. Usually when you draw it with a strong terminal, it winds up being Fishing Village, Hunting Party, Menagerie, Minion, or something else more interesting.
When you want it to be a terminal, it's usually not a complicated decision: There is usually one that stands out that you want it to be most of the time. But it's nice not having to actually buy those terminals and risking them clashing.
But you have to watch out for one great defense, which is having the other players exhaust the cards you most want to mimic. If you need Fishing Villages but you're using MoD for them, and then those Fishing Villages run out, you're in trouble.
I also appreciated another little touch: you don't have to keep your trashers around after you're done slimming down your deck. Once Chapel or Trading Post or whatever has done its job, you can use MoD to mimic one and trash the trasher. It's not a game-changing move, but it's a nice, aesthetically pleasing touch.
Ultimately, I think, for me, I think I prefer the invisible copy version and having it work on next-turn durations despite the confusion. I think the card is sufficiently interesting to warrant the trifling mechanics. Thanks for suggesting it, Glooble.