Earlier this year, there was a short one-off, by an author 
whose name I don't recall, where Shinji and Kaji end up 
swapping bodies in an accident similar to what happens to 
Shinji in Unit 01. 

I remember this. I think the title went something like, "If I Were You And
You Were Me". Can't be sure if it's the other way around.

As for the possibility for a romance between the two, the only thing close
to acceptable (which is still far away) is change either one's age or be a
damn good writer and keep them the same age.

As for ELL's list, you can add:

Tenchi and Sasami  (either 16 to 8 or 16 to 700 differences)
Kaoru Kamiya and Kenshin Himura (ten years I think)
May 'Minnie' Hopkins and Ken Taki (16 years)

-- 
Mark Ferrer