I tend to think of Meyer's and Marozzo's rappier as more along the lines of the side sword, though that's not really a period term. I was referring to middle tradition of rapier, after the era of the side sword and before the era of the transitional rapier that evolved into the small sword. Man, Kevin, the engagement range of the middle rapier is really something, I think the biggest eye-opener for me was not with lunging, because I had a brief sport fencing background before getting involved in HEMA, but the deep body leaning at the hips and waist that really gives you a long reach, combined with the shifting of torso with the use of the legs. Also, using a weapon the length of a longsword in one hand helps as well, but it only helps, you can't rely just on the length of your weapon.
You could also think of your off hand as if you were born with a deformity and that it was conjoined with your chest or face.