I've been experimenting with this card:
Royal Scepter
$? - Action
Reveal cards from your deck until you reveal an action card other than Royal Scepter. Discard the other revealed cards and play the revealed action card twice.
I suspect that $4 is the right cost, because it's roughly as good as Throne Room. The primary differences seem to balance each other out:
(1) Throne Room can be drawn in a hand with no other action cards. When it does, it's a dead card. Royal Scepter is never dead unless there are no other action cards in your deck. This can happen if you draw all your other action cards in the same hand as Royal Scepter, but this is a much more preventable situation. By and large, Royal Scepter is stronger in this case: it fails much less often, even in action-light decks.
(2) You have greater choice over what action Throne Room doubles. If you have Throne Room in hand with multiple action cards, you can pick the action card that will do the most for you when it's played twice. This includes being able to play it on another Throne Room. Additionally, you can choose not to play the Throne Room if there aren't any action cards you want to play twice (e.g., Remake). With Royal Scepter, you usually have no control over what action gets played twice.
Allowing Royal Scepter to work on other Royal Scepters is an option, of course. I've tried it that way, and it requires a whole lot less bookkeeping than Golem would, if it could work on itself. But it's still kind of a mess to untangle, so I think it's better not to allow it.
Regardless of that, though, $4 feels right. But I'm not confident about this conclusion, even after playtesting, so I thought I'd throw this out there to see if anybody had any thoughts about it.