I think I may have stumbled upon a glitch where even though I didn't have enough towers to build I could keep adjusting the path. Then after the next run I was able to spam like 20 chickens. Not that I'm sad about having more chickens, but it kind of made things much easier.
I really did like the idea behind shifting their path as I placed my towers. The first time I played through it I didn't factor this in and lost out pretty quick. Without the cheats I found, I think this would provide a long lasting strategical test. Great job and keep it up.