This has been a big issue for me, namely because I like to stand often when I ride.

I came to the same conclusions as the other posters: the only way to cut down on that "whippy" feel on a loaded bike is to have a super sturdy framed bike. My 25" Trek 520 does not fit the bill. With a load, that bike is all over the place.

I almost bought a Thorn Nomad since they are supposed to be very sturdy, but I tried a Burley Nomad trailer and it solved all my problems in that particular area. The bike rides almost like it's unloaded when towing the trailer, no frame flex at all. I can work it as hard as I want and it's solid.