Good thread Nick.
On a couple of occasions I have had to copy the record because that was what the band wanted; and paid for! But I can't say I like listening to a player (guitar or steel or whatever, but mostly lead guitar) that slavishly copies the record when playing covers. I know a few that do this and they're good players, I just would prefer to hear them being "themselves".
But you added the additional word "iconic" into the mix and that needs to be considered separately. I know a few iconic parts that are intros, and if it's perceived as integral to the song you probably have to do it - but there's not many songs where you can't play your own solo for the lead break. As much as possible - be yourself, I say. Your's may become a better "icon"
And remember:- there's nobody can play like you better than you can!

As a PS - maybe we need a separate thread to share some of our favourite solos?