Right. It won't be a quick thing to do, but I'm pretty sure it'll work.
Firstly, you have to create a new unit entry for each and every combination of Civ/Great Person. With even just the default civs this will mean you'll have to make 85 new units, though they should be very simlar to each other in most respects.
Each great person can have the same unit class as all the other great people of it's class, but must have an individual unit type, for example: <type>UNIT_ROMAN_ARTIST</type>, and each one must have it's one set of unique names. Remember to fiddle the art files as well (another 85 entries, each with the same attributes, but different types)...
If you now add the units as unique units to the civilization they belong to, it should work.