First off I've not yet got the game so probably don't really know what I'm talking about, but this just occurred to me as a possible idea to mitigate the problem with a character not being able to do the thing they are specifically designed to do purely because they just opened the door and so are now inactive.
Could you introduce a house rule that players are able to buy the same skill twice, if any skill has been bought twice it can still be used even when the character's activation token has been used?