What if the slots weren't about what the dragons know but about what shout you are learning now? Say you have shout #1, and it has 3 parts that need to be opened, and the game is just focused on the Shout you are learning now. Then you could kill any dragon and it wouldn't matter because it will still open only one of the three slots you are currently researching.
Perhaps when the dragon dies you learn about which wall to go to to read his words, but that wall is automatically assigned (via Radiant Story) to be a wall you haven't visited yet which will now contain the words you are currently researching. So then that way, killing any dragon is always immediately useful and quest related, and no time will be wasted hunting for the "right" dragon. Because it's always the right dragon for the shout you're currently putting together.
Just my theory.
:thumbsup: I think this is probably the best idea yet, at least in terms of how likely it is to be accurate. This is because it avoids the following sort of situation: under the sort of system I proposed, it's possible to learn two words for each of twenty shouts - you'd have done a whole lot of dragon killing and wall-reading, but you'd still not have any dragon shouts.
But your suggestion seems a little more rewarding, because you'd be learning dragon shouts at a fairly regular rate.