Nice frame, where you not selling this last week ??
I suggest you do with it whatever you like, it's your bike, but as you are asking personally I think the whole brown tape/brown saddle/ bullhorn look is more of a fixie thing to be honest...
I would personally go for a more more traditional, Benotto/ Tressorex/ Brooks/ Cinelli look, but hey, do whatever you want,you choose, Great bike!
+1 on dropping the brown bar tape. I don't think it's really authentic - don't recall many old pictures of bikes with
brown bar tape.
Personally I would go for white tape as a conservative choice, or either blue or red, which would compliment the celeste colour nicely.
In any case, welcome to the world of retro bikes, that Bromwich looks like a good place to start.