I never really had a problem with the old one. Personally, if anything, I would just update the graphics on the old design to retain consistency.

But if you wanted to play with alternate or even radical new intros for Ady, here are some possible ideas:

(1) being that these are edits of films in the late 1970's and early 1980's, maybe make the graphics reflect that (like the Bolson Media Company logo in the beginning).

(2) design a logo similar to what could be done in the 1980's. Not so much new age-y or cheesy, but what you could see 20th century fox or Warners doing if they did a recreation of their logo.

(3) Adrian is in the UK, so maybe make a play with that (the shape of Britain changes into Adywan, like an accordion).

(4) then again, you could always do the logo like the first New Line Cinema logo.

As for myself, I would just slightly update the ANH:R logo.