IMO the problem isn't that it would slow down the game. It's that this card gets shut down so, so easily. It wouldn't be difficult to hold back a few Copper so that there is no wasted coin. In the rare cases where you can't help but lay down extra money, your opponent will have to have Tithe in hand to get anything out of it. It's just not going to work.
You can reveal it on yourself as well, which provides a bit more strategy to the storage idea. I imagine that trying to play around this card is, like you suggested, not that hard, but it'll have its chances in multiplayer to get going, and in two-player the self-storage plan could prove to be quite worthwhile. I'm wondering if it's
too good on that front, giving up all your coins this turn for a chance to spend them in a later turn. It's a bit like Tactician in that sense.
Also, the +2 Cards seems out of place with the tokens-for-money.
Making it +$ was out of the question since the latter half is already doing that, and meshing the two feels awkward. Making it a cantrip could work, but multiples don't do much with each other in that capacity, which isn't to say they need to. +1 Action, +1 Buy was a strong consideration, but I just didn't feel the Forager route was as interesting. With just the plain +2 cards, multiples have the interesting synergy of being useful when draw together, should you want to waste some $ for the turn. With everything else going on with the card, drawing just seemed simplest. +1 Action, +1 Buy has a really good chance of being the right answer, though.