Here is another idea that came to my mind.
Lances are used by one hand on horseback. It gets good reach with that animation. No problems there.
What about a weapon mode to make lances used by both hands on horseback? Very similiar to hafted blade, but only with a thrust and at a small angle only. If we define the angle by clock, I'd say between 10 and 12.
Also, it should be a slower and less damaging attack than usual. So it won't be a noticable edge for lancers over the other types of melee cavalry.