^ this. In essence, some unique buffs will filter through when upgrading your unique units. I understand though that this is probably not quite enough for you.
Therefore it made me think of the following suggestion. What if there were unique units that could build unique tile improvements (like great people) that would be called military training Academy (or similar)? These training Academy tile improvements could work like the native villages of civ iv colonization (for those of you who are not familiar with this, you could send one of your units at a time to these places to learn a new skill after staying put for 10 turns or so).
The training Academy could specialise in training the particular buff that your unique unit has, and would consume the unique unit once built.
For example, a jaguar warrior builds a military training Academy (and thereby disappears off the map). Each unit that you send to that tile in the future can stay there for 10 turns in order to pick up the abilities to fight in jungles/forests more efficiently, move through jungles/forests at double speed, and heal 25 HP upon killing a unit.
Comments/feedback/likes/dislikes?