Yes, it sounds like what you are describing is halfswording. It is easier and more powerful with a bastard sword (which is a tapered longsword), but originated and was common with long- and greatswords, which were better for taking down unarmored opponents. (The bastard sword was inferior at anything but half-swording).
The time period in which axes were more common than swords was not the same in which half-swording was a general technique - swords became quite ubiquitous during the High Medieval period, and half-swording followed after the universal adoption of full plate, which is closer to the Late Medieval period, I believe.
Döbringer called wrestling during swordfighting simply "rangen".
It is generally assumed (or should be assumed) in any RPG where someone with a longsword is fighting someone in armour that the swordsman is using half-swording techniques. Plate armour is particularly difficult to pierce, and the advantage of half-swording is that it offers one much more control over the point, making it easier to jab into the weak points at the neck or groin of an opponent.
Were a combat system to be "real", it would be virtually impossible to hurt someone in platemail without using half-swording techniques. An axeman would not have half a chance against a knight with a longsword in full plate on a dry field - his axe would be virtually useless against the plate.
If you are interested in a more combat-accurate RPG, I recommend Driftwood's The Riddle of Steel. It has the explicit approval of The Association for Renaissance Martial Arts.
So that's today's history lesson, wot.
