Disabling Cain

It makes me really sad when the consensus on a beloved game is that a certain house rule is absolutely necessary to maintain balance and/or fun.

The latest victim here is Battlestar Galactica and our dear Admiral Helena Cain.

I was trying to get a group of people together to play a game, with the Pegasus expansion, in an as-unmodified-as-possible state, but was met with resistance on the issue of Cain.

Her Once-per-Game ability is the "Blind Jump": Blow up 2 random Civilian Ships to jump the ship as an action, to whatever the top card of the destination deck is.
All other things being equal, it counterbalances her penalty, which is that she can't push the FTL button or use the Engine Room.

The imbalance arises because of the action "Launch Scout". It's a purple card, and she draws as many as 3 purple on her turn, so it's going to happen.
So, she can look at the top Destination Card, leave it there, and significantly lower the risk of the Blindness of the jump. It may still take a few actions to find the perfect destination, but as long as she's proven herself to be human, the rest of the group is probably going to be agreeable to cooperate in scanning for good places to go.

That's the background. Most BSG players are well-familiar with the issue.

In addition to the fact that she's top in the order of succession to be Admiral, it does kind of make her a no-brainer choice, compared to Adama and Tigh's abilities.
To be honest, I don't mind this being the case, but I can see why people demand balance.

It would make me happier to get Official Errata, or some sort of clever in-game fix in the Exodus rules, than to have to resort to choosing one's favorite house rule fix.

The commonly-accepted "fix" to Cain seems to be to shuffle the Destination Deck (possibly except for the bottom card, in order to keep another ability useful) when she uses her ability.
The thing I don't like about this is that the previously-skipped destinations go back into the mix and that's a larger change on the game.

I came up with a very simple fix of my own:
By nature of it being a Blind Jump, you simply don't let Cain Blind Jump while she knows what the top card of the deck is.
That is, when she looks at the top card, she gets a marker. When the top card goes away, she drops the marker. If she has the marker, she can't use this ability.
That seems to me like it would have the least impact on the rest of the game, and wouldn't affect Cylon Cain's decision to never use the ability, for example.

Does anyone have an opinion on this?
There may be a "part 2" to the post with more suggestions...