Well first off, happy new year's eve everyone. I wish I could've done more Gaia but with the short amount of vacation and school work to do, there's never enough time off it seems.
There's a lot of theories as to what he said. I think there was an interview with the story board director (he did a great lecture series on Gainax's methodolgy, link here:
Eva Geeks - Tsurumaki lecture series) that said something along the lines of "I couldn't have done this without you".
I know many others believe it was more personal than that, since they did had an off screen sexual relationship but again, even with official backing, I wouldn't have a reasoning for what he said or why. It's like who shot Kaji; it was there for the purposeful artistic flair of open-endedness.
This kind of stems back about all the relationships too; none of them are concrete or official. We can interpret them many ways but in the end, there was probably no intended 'official' pairings beyond the ones for the side characters.