I think the diplo units should operate solely in a modded espionage window: it would retain the production->influence mechanic but remove the micro of moving the unit into the CS' borders (which is a turnoff for some I've heard). Presumably the AI will be evn more capable of using this system over the current one as well - no more diplo units standing around cities or outside of CS borders. If implemented, I would suggest that the first limiting factor should be a "turn to arrive" number, representing travel time*, which would speed up through the eras. It may be feasible to have new diplo units increase influence amount as well (finally!). Another thought: diplo units could be stationed in CS cities on missions to slow influence depreciation and/or intercept and sabotage other civs' diplo units attempting to gain influence. Sorry for the unstructured brainstorming (and not actually answering any of your questions
), but I see so much potential here! Heck, you might be able to give diplo units diplomatic actions with other major civs as well.
*Actally, now that I think about it, this would be great for all diplomatic actions, it would make the game a great deal more immersive..