I don't like turning off the "save random seed" option either becuase I feel that saving and reloading is not fun and a waste of my time (I am lucky if I can get more than an hour per week on the game now, and if I do nothing other than save/reload I feel cheated). I used to be a save/reload nut on previous versions so I appreciate the extra skills I picked up being forced to play the game through after losing my best units.
However, the poster tried for an HOUR to change the result by a save/reload so I figured I would help out.
Back to topic, my favorite counter against archers (or longbowmen) fortified in a city is the city raider III promotion. The units that will clean a city out before catapults are the CR promoted axeman and swordsman. You can even build experience against barbarians and animals with a warrior and upgrade the unit into a city killer later.
And you can keep the promotion if you upgrade to a unit that doesn't get City Raider naturally. That way, you can use them even more effectively for city cleanup AFTER catapults.