Thank you both, I'll make another chien and play about with it a bit. Reducing the diameter of the tirant peg also makes a lot of sense.
But the comment about notching the chien so that the string is actually pressing on the wheel leads to another query - should I do the same thing with the other drones? at the moment the top of the bridges are flat, so that when I engage a drone the string is straight from tailpiece to nut, just touching the wheel across its width. Should the bridges be notched to hold the string in, so that it as actually pressing on the wheel, in the same way that you describe for the trompette?