I've been messing with space stations recently and I would say that Rail Platforms that could be used to lift Mechs without any weird side effects would be a really welcomed addition to the game, by me at least.
I think what is causing that amusing leg shifting dance is the platform size to the mech's bottom size. The platform is, I think, five blocks wide while the mech is somewhere around seven to nine blocks wide. If I am right, this could be fixed simply by making a wider platform. Or it has to do with the mech being moved about like that which would very likely mean there is no fix for this.
I tested mechs on larger, thicker platforms. It seems like the funny dance is a result of the platform's horizontal movement rather than size. As such there is likely no way to fix it (not one that I could think of any way.)