I've been successfully commuting (11 miles each way) on my touring bike recently, but there are days when I need to carry more weight or bulk than I can comfortably put on that bike. I've been looking at long-tail cargo bikes but I'm considerably put off by the amount of flex that I feel when the bike has a load on it. Unloaded they ride great, but when I put 50 lbs or more on the bikes, they begin to wag behind me - especially when I'm climbing hills out of the saddle (which I like to do). I've tried both a Surly Big Dummy and an old Xtracycle with the same results. I also tried a Yuba Mundo. The Mundo did have less flex but it was heavy and I prefer the more forward riding position I could get on the other two bikes.

Do I just need to accept a certain amount of flex?
Do cargo bikers avoid standing up to pedal?
Is there a stiffer bike that I should try?