Persians v Britons post-imp castle showdown???

I played a game the other day as Persians against Britons. At the end of the game, it was this horribly tedious impasse where I kept trying to treb down his castles, but his trebs were warwolfing my trebs down over and over. I couldnt dive to hit his trebs with my cavaliers or hussars because he had halbs protecting them and the castles garrisoned with longbowmen+murder holes that would shred any other units I sent underneath.

In the end I won because I was able to decimate his eco and keep mine going, but without that I probably would have been toast. How could I have dealt with these castles faster? Bombard cannon? Rams? something else entirely?