First off, I am a G.K. Chesterton fan as well.
It sounds to me that you really did pack the bowl too tightly. Smaller bowls are a little trickier to pack, since any top pressure gets transferred all the way down to the bottom.
My advice is to try this: After drying your tobacco, just let the first third of the bowl pack by gravity. Just let it fall. Pack the second dose with your thumb or finger, but just lightly push it in. Finish packing the bowl with the pressure you are using right now.
When you light, the tobacco should swell up out of the bowl, so very lightly tamp it in. You may need to relight here, but this should get your smoke going.
Take your time, don't get impatient with yourself, and enjoy your pipe! Cheers!