Hmm, Maybe something like this:
Four imps (mini-meeples), who lives at inns (they help clean the stable and other such tasks). One imp on one road give you one point when the road is finished, two gives two points, three gives five points, and four gives ten. However - if anyone but the owner of the imps (there could be several differently coloured imps on one road) finishes the road, the points are negative (for the imp owner). An alternative could be to have the dragon move one step for the first imp, two for the second, three for the third and five for the fifth - it will always mo toward the closest imp and it will not eat anything else but imps. (Imps are videly regarded as snacks among dragons - trust me I know these things.)
Now - I have not thought this through, but it goes in line with the mischievously nature of imps. And - we avoid calling them
children (which is almost a curse word)! Feel free to comment, steal or disregard!
This will also give you an incentive to play the roads as they should be played: roads do not stop in bushes